 Okay, the rate of new people seems to have slowed to something reasonable. So I will start. And so it's my pleasure to introduce Glenn Whitney. He has played many roles, including being the founder of the Museum of Mathematics in New York, but recently he's been doing a lot of very innovative and creative mathematical constructions with different units and has taken on the challenge to do one of those with us all not in the same place. So I'm very excited to see what we're going to be making with these interesting pieces. And I also want to take this opportunity to thank Glenn. There was a quite a big group of us who were organizing this workshop, but we didn't really have any leader, and he has he really stepped up as the person who kept us all on track and made sure that everything got done. And so thank you so much for that Glenn. And with that said, I will pass you over and I will be monitoring chat and so on. So if you have comments or thoughts to put them in there and I will communicate those to them, but thank you and pass you over. Well, thank you so much for that very kind introduction. I'm just happy to be a part of helping this community together. And I wanted to start with sort of the setting and context and like why I think it's worth doing this and so on. So, and again, you can see this is the URL modular not origami just after the main website, and I will go full screen so we can see oh I need to share, you can't see a thing yet sorry. Just a second. Okay, share screen. Okay, there now I think you can see it. I'll just put modular dash not dash origami after the main website, and you will find this. And here we go. So, there are lots of different paths that come into mathematics, many of us here have come in through traditional academic training, and that's one good way. But many of us here have sort of arrived at an interest in mathematics through other routes. And I'm always excited and interested to see those routes that arise kind of organically from some other pursuit that doesn't perhaps initially seem to have anything to do with mathematics. And I've just shown some, you know, example pictures from a couple of those things here. These are all kind of things that you can find out there in the world, or on the web, that clearly have some mathematical structure or content or mathematics can be brought to bear. But again, where the original pursuit wasn't consciously about mathematics. So we saw another wonderful example of this in Bernal Noel's excellent presentation yesterday. So, and there's many more I can put up here. I obviously can't, you know, do complete justice to this. But one of the reasons that excite me is because when I see things like this I think, aha, this is an avenue that I could try to use to bring new people into mathematics and get them excited and at least to understand what mathematics has to offer, because maybe going straight in the front door mathematics might not grab their attention. But starting with something that even if a person is not already into beating or not already into dominoes or whatever it might be, they, you know, that might be more engaging to begin with and then I can say aha. And look, it's really it's math that drove this. So, you know, you can imagine my delight when I see pictures like this that and here's a whole smorgasbord of, you know, mathematical objects again that came out of this pursuit of origami a particular sort of branch of origami called modular origami. And they're just out there and the people who discover them and create them produce them aren't necessarily coming from a consciously mathematical background. And most people have fiddled with origami at some point in their lives and maybe they made a crane or at least what we used to call a cootie catcher at some point so this is not a foreign notion and they know that makes interesting things. It's a really accessible way to start to get people at least comfortable with the notion that mathematics, maybe have something to offer them and can help provide beauty and enrich their lives so this is all good and in particular, when I saw this piece, which you can you know Pinterest or Flickr so on. This is a design by Roberto Gretcher and this actual folding of this particular into pieces by a person named Michel Piccola. When I saw this, you know, I really felt that this was something to aspire to because there's so much. First of all, I think it's beautiful. But second of all, there's so much going on here mathematically. So if you count, you will discover that they're exactly the same number of pentagonal openings as there are heptagonal openings. And of course, those of you who have the requisite topological background. So that's absolutely not an accident. No matter what tourists we make from these units that can only make pentagon, hexagons and heptagons that they will always have to be equal. If it's if it's a tourist shape. And that really is a nice intro to some some fairly deep parts of mathematics so so there's so much going on here. And it's a nice big construction this one has 555 of the individual units. And so I thought, Oh, this is something media if I ever get a nice big group together. I can just have them fold these up and and we'll just assemble them together and you know create this beautiful structure together. So, you know some time passed and I got a call from a high school in Manhattan they wanted me to come and do a double period session with two math classes so I'd have about 60 high school students together. And I thought, you know, 555 over 60 that's less than 10 a piece, hey have them make a dozen each just to have some extras and double class period and I timed how long it took me to fold one of these is like, no problem this will be a piece of cake. And for those of you who have been involved in some of my events you know that sometimes I veer toward the slightly ambitious and so here's what ensued. Certainly pictures fail me here because I in the in the midst of this other chaos I failed to record it photographically. Some people were just sort of dropping their finished pieces on the floor. It took a little longer than I had anticipated to get the folding down with the with the students. And by the end of our double class period. We had piles of crumpled paper files of folded paper, and we had maybe about a seventh of a Taurus that had actually been, you know connected together. So, fortunately, there is a there is a good save here, a dedicated subgroup the sort of math club of the high school, sort of swept up all the pieces and then devoted their lunch times for the next roughly three weeks. And completed well this is actually six sevenths of the original originally planned unit but it was still enough to to fit around into a Taurus. And they did eventually, you know, finish off the object, but nevertheless that was six years ago, and I have not between then and now done an event with these units. So we'll see if I can sort of break the, the omen of the last time I use this type of unit for a construction. So, there's obviously an obstacle here that the the the interesting part for us was how these units linked together and how what you construct from them and to see that construction come together and then to start to be able to make some interesting observations about it. So, I needed a way to overcome that obstacle of this initial folding step and getting these 555 pieces together. And, but I didn't quite know how to, you know, how to, how to get over that hurdle. So it took another piece of chaos to help me over the hurdle. This is a picture of a sort of, it's often the corner on the lower level of the museum of mathematics in New York City. I may not have noticed this little bit that's, it's usually cordoned off, but anyhow that's a laser cutter, and it's next to this exhibit on on the right, which is called tile factory and it's there because in tile factory, there's sort of a free form program that'll let you make a tessellation based on, you know, one of the gives you a few different wallpaper groups that you can choose from and then you can sort of make a free tiling that will have that wallpaper group of symmetries. And then the idea is that you could, once you've created a tiling you could actually have the immediate satisfaction of having your tiles cut out of some material and then you can play with them and fit them together. So this is all good and and when there's somebody there, we couldn't make itself serve somebody asked actually run the machine and anyhow, one day in the middle of a busy crowded day at the museum, the laser cutter literally caught on fire. There were, you know, flames coming out of the top of the machine. And so I said to the folks that run the floor like, maybe we shouldn't actually use a laser cutter maybe there's some other technology that could could be safer. And that's what got me interested in these ideas of automated cutting machines. So, you know, you put in a sheet of something and it's actually got a physical blade that is run by the computer and cuts pieces. Although as far as I know there's still a laser cutter in the basement of the Museum of Mathematics. That got me interested in what these machines have done. And fortunately, because they become more mainstream, people use them for crafting and they become they become popular in a mainstream way, then there's been a huge arms race among the consumer level cutting machine manufacturers, they've now become quite sophisticated. And so here is what is hopefully the chaos reducer. This is the machine that cut all of the pieces that you all have. And hopefully is going to free us from a lot of the time and effort of doing all that folding. So that means it's time to build, I'll stop the share. And for a lot of the rest of the presentation, you're going to see more more my hands, then you'll see my face, hopefully that will be useful. So I will switch to the hand cam. And here you can see sort of a diagram. And it actually if I switch back to I'll share my screen real quick. One more time. So if you go to the homepage and then click on the module origami, you'll see there's a list of polyhedra we're going to make genus zero polyhedra I keep things simpler. So here's a list of polygons for us so you can see a list of polyhedra that have only have to hexagons and pentagons those are the those are the things that our units will make. And you should pick one of these as your target, they're arranged an increasing number of pieces required. So here's a straight up to a deck of hedron requires 30 pieces, all the way to if you're truly ambitious you've received just enough pieces to make a full soccer list of hedron at the bottom so I'll let you pick your your target. And now stopping the share and going back to my printed diagram. Yeah, going back to my printed diagram. I've just print out a copy of the diagram and I've labeled it with the colors that I'm going to use. So I've chosen a relatively modest one. This is the triacus tetrahedron truncated triacus tetrahedron. And this will be my guide for building so if you've had a chance to do that great if you haven't. Well you can either try to do it on the fly, or you could follow along and exactly replicate what I'm making. That's up that'll be up to you. And I've, I've punched out a bunch of my pieces as I had suggested you might want to do in that page, but understanding that some people's pieces arrived just today. And other people may not have had a chance or might not have noticed. We'll start with punching out some pieces. So you should have sheets that look roughly like this. And you can see the rectangular pieces in here. And the idea is they should pop out easily, but sometimes they don't pop out quite as easily as you might want them to. So there's two sides, the sort of, if you will convex side, which sort of the bumps are towards you, which is also the side where you can really feel the cuts with your fingertip, much more than on the back where they're smooth. We'll call that the A side. And when you're looking at the A side, if you fold the little cuts away from you, so make mountain folds out of them, that really helps with the separation. And then you should be able to just pull apart, and they should start to just come apart and then the straightaways definitely come apart more easily. So these little divots can be a little harder, but they should separate fairly easily. If they don't, you may need to fold them back as well along those diagonals. And you might need to maybe put your fingernails on opposite sides of the sheet and push sort of perpendicular to the sheet, and they should come apart. You should get a supply of these little rectangular pieces like so. If a little tiny corner breaks off, it's, you know, it's not going to be, it's not going to prevent your construction from coming together. Okay, and so that would give us an individual piece like that. And so the minimum of these you need to actually make a closed polyhedron is 30, if you're going to do the dodecahedron, I have 42 prepared. And, you know, and I understand that, so there may be timing differences here, some people are, are pulling pieces out. And that's okay. There's going to be a fairly wide range of finishing times. So I am hoping that we'll get a number of completed units so I can get a nice little group photo. And if we complete, let's see, what's six sevenths of 555, you know, some something in the high 400s. So if, you know, at least say 15 of us completed dodecahedron or larger this will set a new personal record for events that I've led in terms of number of units use so there's a very modest goal. I can make it over that and I love to get a group picture of some people's constructions at the end in gallery view. So anyhow, this is a single punched out piece. And you can see there are some internal slits that are important. So I want to do the same thing with those. I want to just fold them away from me when I'm looking at the A side, and just open those up because I will need to be inserting. You know, the tabs in the slots as they say. And I'm going to just open these all up. Okay, that's good. And I'll get these these tabs in the corners here I want to slip those at all. And you may notice that the tabs in the corners, where they reattach back into the main material. There's a little sort of inward divot there, and you want to try your best to get that punched out to the extent you can. Definitely you want the tabs to narrow a little bit there, because of course it's that narrowing that keeps them in the slots. Once you have it connected you want to have some mechanical force, keeping it into the slot. So that's why it's important to try to get that divot separated. I've got both of these corners. And then in the middle, there's two additional tabs that are made up out of the material of the unit. And so you want to disconnect those as well so that they can, you know, sort of flap freely out like that. They are attached, you know, along the base so so so they're sort of only cut on three, three edges. So don't don't rip them out too vigorously, because they need to remain attached and that'll be sort of an extra buckle that will add to the sort of physical stability of our finished product. So there's a completely, you know punched out and all the cuts separated piece. And although we're not going to really be doing origami, the unit still has a three dimensional structure that's based on certain creases. And so I've created crease lines for you to hopefully make this folding step really rapid. So picking up another piece, the creases lines come in two different forms and I'll explain why in a minute. Sometimes they look sort of like you ran your fingernail over the plastic, like this one does. And other times, they look like sort of a dotted line. And because the tool that I showed you that I that I cut these on had two heads, and I put a cutting tool in one and a creasing tool in the other and it's the creasing tool that made these ones that look like a fingernail, but somewhere midway through the over 7000 units that the second tool carriage simply up and died. So I don't want you to think that this whole talk is a commercial for silhouette cameo pro you're getting the, the good and the bad it did manage to cut all of these but but the second tool died midway so I had to quickly improvise and do this dash cut pattern to create score lines for the remaining units so you may have some of each impact you likely have some of each but anyhow just go over now what folding to do again with the a side up. So it should be slightly curved away from you or you should be able to feel the rough edges of those openings. You want to first make a mountain fold so fold away from you so that the two ends of the piece exactly line up so you just you're just folding in half. It's a long way or with a short fold and there should be a crease line there that will help you do that very easily like so. And the other thing to notice about this, when you complete the crease is that and one end of the piece will be a little divot just to the left of the crease, and at the bot at the other side will be a little divot just to the right of the crease so this central crease exactly splits the divot so it doesn't go from the innermost point of the divot to the innermost point of the divot, it goes just between the two divots and folds the piece exactly in half so that the end matches up. So that's the first fold. The first folds are in the opposite direction and you can see that the crease lines that what they're going to be, you're going to make a diagonal fold here that brings the left edge along the where you made the first fold, like so. And again, you'll this time, you'll see that the folds go right to the center of the divot. And that's sort of why the divots are there is to kind of help you make that that crease, and then you can flip it over and you fold the tab, exactly that same way so it makes a little kind of triangular pyramid here, just like that. You do exactly the same thing on the opposite side. You can just turn it over. And again we're pulling the opposite direction of this top crease we're bringing the left edge up to the top, and just folding along that existing crease there. And then I can flip it over and do the same thing with this tab, bringing it together like a tent. And that is a piece that's now ready to put together with the other with the other folks. And this one I didn't, you can get, it's easier to, sorry, it's easier to divide these slits when you have the piece flat, but on this red one I forgot. So it is possible to open up the tabs, and so on, and the slits after you folded it, it is as you can see it's a bit trickier. So I'm going to go ahead and do that with this one. So in the spirit of your learning from my mistakes, do try to remember to separate your slits and tabs before, before folding. Okay. And finally, these buckles, the buckles are actually the hardest after you folded it because they're in such tight folds in the center. And also notice that in order to fit the sheets into your, into your packs, you'll find that the center fold is already folded on on some of your pieces. Right when right from the get go. Okay, very good. So that piece is complete. And just to recap, so that you can see the whole thing again. I'm going to go ahead and do the folding on this pink one as well. This one is the other style of creases with the with the cut lines. So I've got the a side toward me. So it's curving away from me. I'll now fold away from me to make a mountain fold along that dotted crease line. I'm going to go in this direction, bring the left side up to the folded top. And again, I should find the material will just naturally want to find that pre scored crease. Flip it over. Do this tab here is this pre scored crease. So, I can do the same thing on the other side, bring the left edge up to the top fold finds the pre scored crease, flip it over. Bring the tab down. And I get another piece ready to ready to construct. Okay. So that's how you, yes. I think people are asking to see one of the finished units a little bit. So maybe if you can just hold and rotate that one to. Okay, yes, very good. So it looks sort of like two upward pointing pyramids connected by this seam in the middle. So you know you've gotten all the folds correct direction when it looks like that. But there is a handedness and you, if you want them all to be the same handedness is me that's why I was emphasizing the side versus the B side. So you know you're the same handedness is the ones that I've got. If, when you look at it from above like this with the two pyramids pointing to you toward you, if the tab on the left is, you know pointing up or away from you. You know the same handedness that I've got if you if you reversed all of the folds on every single piece your construction would also work but it would have the opposite handedness. But the key thing is that every individual one that you fold together has to have the same handedness. And if I rotated around here's what it looks like, you know from the underside, and, and so on. So hopefully that makes it a little clearer. Should I go through another one, the folding from the top. Can I ask a clarifying question. Sure. So right now, none of the tabs should actually be inserted in anything or like that's right we've just gotten these two pieces ready to link. And I recommend that you have at least three completely ready to link before you link anything. I'm linking some things up in just a minute. But yeah I do recommend you have at least three ready to go before you start. Because in the final constructions, as you might gather from those skeleton diagrams of the polyhedra, it's always going to be three units coming together. And my recommendation is in general, complete any vertex you come to any vertex you start to link up, you know, go ahead and link that up completely. Okay, so I'm going to refer to my drawing diagram and I'm going to make sure that I have three ready I have a red and a pink ready. And a red pink junction, and the third one in my diagram at a red pink junction happens to be green. So I will go ahead and do a green one. And so I'll make sure that I have gotten all of the tabs separated and all the slits opened up. And you may find as you're doing this that some pieces just some colors, there's come apart a little more easily than other colors. And that's for two reasons, even though these are all nominally the same plastic material, not every brand Oh and incidentally for those of you that are interested. What this material is, is lighting gel for theatrical productions. That was the most easily available comes in multiple multiple colors comes on roles so I could run it through my machine and bulk. So that became the ideal material for this particular build, but I could use any machine material that comes, you know, on roles. And anyhow, although they're nominally all the same plastic, maybe the different coloring agents affect the physical properties so you get you get differences. And then of course there's blade sharpness I went through about five blades in the course of cutting all these pieces. And so my apologies there's there is some difference, you know if you happen to have gotten ones that were toward the end before it was changed out or just after the blade, a new blade was put in. Okay. So, again I'm going to fold this I've got the a side toward me so it's curving away from me. I'm going to make a mountain fold in the center to just fold the whole thing in half, like so. And then I take the left edge, bring it up to the top. And it will find that pre score. Flip it over to do this tab to come back toward me to finish off the pyramid. And now I can do the same thing on the other end, hold here. And I can fold this down to finish this. And I've got my two pyramids side by side. And here's what the whole thing looks like. If anybody is feeling maybe a little insecure about whether there's came out. I mean, in a fashion it's going to allow them to link together well if you want to, you know, we can give you the camera, and you can hold yours up and we can verify or if your people are feeling comfortable that's great so you can get the mood of how people are feeling about whether their units are coming out. Sort of like, like the ones here you see on camera. I'm sorry, do the colors matter at all, are they all the same because I don't think they are geometrically identical the colors are for decoration if you want to use a color scheme that brings out perhaps the symmetries of your polyhedron, or if you want to assign colors randomly or there's not enough to make a monochrome unit there's only 18 of each color. So you need to use at least two colors, depending on your polyhedron but the color scheme is entirely up to you. Thank you. So I think the issue of like mind keep breaking is there like any good advice on how to not break them. So what's kind of breaking you are you getting. It's like mostly with the creases. Like the ones that are like inside. If you hold up a little higher. It like breaks like this. So the tab is no longer a tab and it's like a flap. So it broke along the scoreline more. So that minor like I've noticed especially the blue one is like more brittle. Breaking a lot. Okay. Well, under the circumstances I guess my advice would be if you aren't going to try to use all 90 pieces switch, like switch swap blue for another color the physical like I said, I don't have complete control over the physical blue is breaking a lot maybe just swap colors. If the other ones aren't doing it. The main thing that's going to really help prevent the breaking. Again, if you can see here is try to get that as well folded as I can before I separate it. And also when you do separate it the most effective way of separating is one finger nail to the left on top the other finger right on the bottom and push perpendicular to the to the cut there. The breaking is happening when you're when you're popping out this tab right not when you're doing the folding. Right it's like when I'm it's not the tabs it's like the crease or like not the creases but like the cuts in the center for like where the inside like this split right here. Yeah the splits are breaking. Yeah, yeah so fold it like as fully back along the slit as you can before you try to separate it and separate it by pushing opposite directions perpendicular to the plane of the plastic. And then it usually will just only break in a small part of it, and then you can just extend the cut to the end until you hit resistance. So hopefully that'll reduce the breakage for you. And my apologies again with the vagaries of the material. Question, how did you decide the color scheme for your personal. Well the particular one that I'm doing this triacus tetrahedron. I wanted to highlight the fact that originally did come from a tetrahedron. So I colored all of the pentagons that came from one face of the original tetrahedron, the same color, and I use a different color for each of the four faces. And then there are six places that correspond to edges of the original tetrahedron, and I made those the contrasting green color. So that's how I use the five colors for this scheme. So we should in the end see a red face and orange face a pink face and a magenta face. And then you guys don't have green, but I you guys got my blue so I switch green for blue. I'll have I'll have green edges connecting those groups of pentagons. That's the thing I chose, but I could have taken you know orbits under the symmetry group of the tetrahedron. So I could have made it half one color half the other color. I mean, there's, there's lots of possibilities. So in just a minute here once I once I get this one, I'll separate it and folded. I'll show you how they link up. And then, once you can make and link vertices. You can more or less just follow any of the polyhedron diagrams on the web page. Or of course I'll keep a running tally of, you know how I'm linking things up so if you want to follow this triacus tetrahedron that I'm making you're also welcome to do that. Okay, so I've got a little bit of a supply of the folded units now. I'm going to go ahead and go over how they link up. And so you can, you know, watch you as you're as you're folding them up or, or if you have some units you can you can follow along and put together a vertex, as I do. And I'm going to start. Let me just give a little bit of background the the tops of these pyramids are going to become literal pyramids pointing out of your structure. So if I want to be red pink. If I want to be, you know, red pink green going around clockwise, then I'm going to go ahead and actually just kind of fit them over each other. I'm going to fit them over each other in that orientation to begin with. So, yeah, here we go. So I haven't actually linked anything I'm just sort of fitting them together, the way they're going to go so you can see that three of these peaks are going to make a single pyramid in the final in the final construction so they're going to be like that I haven't linked anything yet. And I've got them red pink green in that in that order from the from the outside so this is how I'm going to want to link them. The green one aside because I think it's a little harder to see since it's so dark, and I want to link the red and the pink this way. And so you can see that the red is going to come over the top of the pink in this order. And the easiest way to start is I want to slip this tab which I think of as the, as sort of like the belt buckle into these two and it just, it just goes. Would you make your hands down it's off screen. Oh, my apologies. Okay, should I go back to maybe I should. Maybe I can. All right, now you can see it all right, let me go back to the arrangement that I had, just to make sure everybody can see that this is I was just lining them up to for fit. This is how three are going to fit together. To combine. Do I need more light maybe. Let me try a little extra light see if that helps. Okay, I don't know if that does that make things more visible or less visible, or maybe not much difference so anyhow, this is how they fit together. So here's the green one out of the way, for the moment. So, here are the red piece over the pink piece. And I'm going to want to the, the, the, the sort of buckle of the pink on the inside here slips through these two slits on the red. So it comes from underneath. It comes through both of these slits so it just briefly has just a little bit on the outside so there's just a little bit of pink on the outside of the red which I realized is probably invisible on camera. So let me do it with, let me temporarily do with the green so maybe that maybe that'll be more visible. I have to switch back to the pink to get the color scheme I want. But if I were putting the green here. Like so. I would be separating out this buckle comes from behind. It comes out through the lower slit of the red. So you know it's just peeking outside of the red just briefly, and it goes back in to the, to the other end so I have just now hopefully you can see I've got just a little bit of green showing between those two slits on the outside of the red. Is that at all visible. Okay. So I'll go back. And I actually wanted a pink there. I'm going to slide I'm going to have the red going over the pink. So from the inside, I get the, the buckle of the pink, that interior tab that's sticking out. And then I slide it so it sticks back in through the second slit. And that holds those together there. And then I move over to the main big tab here. And I just go ahead and I slide the point of the main big tab into the big diagonal slit there in the pink. And I slide it all the way in until hopefully actually get a bit of a click at the end. And now these two are pretty firmly attached to each other. And that's the goal that we are going for. And then to finish the vertex and I recommend that you finish the vertex. You know, finish each vertex as you come to it if you can. I'm going to need to weave this into here so the green is going to be over the pink but it's going to be under the red. No, it's going to be over the red, but it's going to be under the pink sorry, my apologies, the green is going to come over the red because the big tab has to go inside there. The pink, the big tab of the pink is going to come out of the outside of the green and slip in there. So definitely want to sort of preview it before you start, you know, buckling anything in. And as with the other cases, you definitely want to do this in this sort of interior buckle first. I'm going to bring the red buckle out through the slit in the green. The red is peeking out. And then I have to get it back into the inside of the green. So it goes through both just like a sort of like a belt buckle. And I won't do the big tabs yet. I'm going to now do the buckle from the green into the pink. And it comes on out and then I'm going to get it to dive back in here. This last buckle can be a little tricky. You have to bend it around to fit through both slits. And there we go. So I've got both buckles in now. And, you know, this holds together but because of the stresses of the whole big polyhedron, we now want to take our big diagonal tabs, exterior tabs, and pop those into their respective slits, and the pieces underneath so that was pink into green. And here is green into red, like so. And that completes a full vertex of my polyhedron, looking like that. So every buckle comes from behind, goes out through the lower slit back in through the upper slit. And then on the other side of the ridge, I have the big outer tab going into the slit. And that's how the vertices fit together. And now I'm just going to proceed around the entire polyhedron. And in my color scheme, I'm going to now next focus on the red, I'm going to do all these red vertices next. So I need to get some of my red pieces folded and separated. So I'm going to do a couple of those and then I'll do another vertex given the chance to see the whole process in action. So the idea is that all the tabs that you're putting through with like the belt buckle and everything. Those are underneath kind of the pyramid that you're forming between these three pieces, correct. And the belt buckle start underneath come out through the lower slit and go back in through the higher slit, whereas the, the big, these diagonal tabs here, those are over the top and the diagonal tabs just disappear inside the underneath piece. I guess. So to clarify, so I'm almost through kind of these pyramids, but these tabs are sticking kind of out on top. Right, so you want to reverse that that one so the blue there should go on top of the, it's like orange. I think so yeah the blue should be everywhere on top of the orange. And then the orange buckle will come out through the blue and go back in and then the big blue tab will go into the, the orange slit from the outside from the outside in. So you want to reverse the, the, you want the blue on top of the orange there instead of, instead of underneath the orange. So then this tab will be pointing kind of going into the interior of the polyhedron not coming out from inside. Thanks. Yep. Thank you for asking. You recommend I imagine to make a bunch of pyramids for you and start putting together shape. Oh, no, no, I'm going to now start from this pyramid I'm just going to start this is this is my, the seed of my polyhedron I'm just going to start adding to this and I'm going to work my way around the whole polyhedron. I don't recommend making a bunch of separate vertices and then trying to link those together because what you'll end up doing is you may make too many independent vertices and because each edge has to link to vertices. You may find that you can't actually link up your final final polyhedron it's much sort of safer just always keep one big unit that you're working on and just work around your polyhedron. So the next thing I'm going to do is I'm going to take this single, you know, one third vertex and I'm going to add two more reds to make it a full red vertex. Okay. So I don't recommend making sub assemblies and trying to connect them because it's easy to lose track of where the sub assemblies actually have to overlap. It's better to just make one polyhedron and just keep adding to it and work your way around the diagram. Okay. So basically if we were making a single 600 piece or more, you know, construction, then I would have pre divided it into modules that that we could build that wouldn't have this overlap problem. But since, you know, we're each making a separate piece, and the pieces aren't so large. It's easier just to always keep your construction as a single connected component. Okay, so that's good. Okay, so now I have the initial part that I've started working on. And I want all of them at this vertex to be read. So now I don't have to worry so much about the order I can just really focus on how they fit together. So I want to add two more reds to this. So to start with one of them, I put it over the top. And that's the easiest way to think about it is the, as you go around, in this case counterclockwise, each one's over the next. And I will start by putting in the buckle. So the one that's underneath comes out through the lower slit of the pair, peaks out just briefly, and then heads back in if you ever if you've ever tied a knot that's called a bowling it's the other is the little mnemonic about the rabbit pops out of the hole goes runs around the tree and then pops back in. So it's sort of like that it comes out of the slit looks peaks outside and then pops back in. So I'm going to grab, we'll just fit through the big diagonal slit on the outside. And now I've got two out of three for this vertex. I'll rotate it a bit, put this one in place again it's going to go over the top, except, of course, the very starting one has to go over the top of that that's how you get the weaving. The weaving really helps strengthen the final vertex. So, you know, before I've done even any of the tabs that actually kind of holds in place. See, I can turn it upside down, it won't go anywhere, even without having done the tabs it kind of holds in place. So, in other words, this one is over that one. And this one is over that one. And this one is over that one so they're each over the next one around in a circle. And it's that weaving that helps strengthen it. Now, of course, now that I have it in its spot I do want to actually put the tabs and so it'll hold together once I make the big polyhedron. So I'm going to come out. I'm going to pop back in through that tab through the side of the higher slit of the pair and pull it through from the inside. And then I'm going to take the big tab and slip it in the big diagonal slit. Pull it all the way until it clicks. And finally, I've got this one more. I gotta find the buckle from the inside. I gotta find the slit stick it through it's peeking out. And I want it to go back inside. The third buckle can be a bit tricky to get to get in but there we go I've got it in. And finally, the last big outside tab. I'm going to get slit until it clicks. And there we go. Now I have two adjacent vertices of my polyhedron, like so. Now just for ease because the those monochrome vertices are the easiest to build I don't have to worry about the color order. I'm going to go ahead and sort of do the whole red section of my triacus tetrahedron. And so holding it so that it matches my diagram. And here I want on this here I want to put two more reds. So I'll get those ready and then I'll add them on. So at this point, this is the whole construction mechanism, except for closing a polygon. And so you have to just keep track of the number of polygons that have gone around in a ring and be ready to, you know, do that closure. And when when the time is ripe, so to speak. So it's easy to like lose count and end up with a hexagon where you meant to have a pentagon or a heptagon which is not going to be very good for us, since we're trying to do positive curvature, where you meant to have a hexagon. So when I get to the first point where this closes up. I will, I'll definitely highlight that. But so anyhow just you can feel free to just start working your way around your polyhedron. And you know, connecting up, you can do random colors, you can try to make a color scheme. And if you close up to a pentagon every time it's possible, then you will very naturally just get a regular dodecahedron using 30 of the units. That's sort of the briefest version of this. Now what we need is some music to build by so if anybody has you know good tunes they want to put on. I've just opened up a bunch of breakout rooms so if you if there are smaller groups who want to go into those and chat as you make. You can do that without disturbing the group as a whole. And then there's a broadcast and announcement if there's anything that you need to be coming back to the main group to to see. But yeah if you want to go into smaller groups and talk to each other for your free to pick a room and jump in. So here I am doing another red vertex up here. Looks like I missed a slit. Can you just quickly show your diagram with the camera so I can make a screenshot. Oh yeah, absolutely. Let's see. Is that big enough there. Yeah, wait a second sir. So I'll put that in the chat. Okay, sounds good. Okay. So here in this room you can see I now have this mixed vertex to read vertices. And my next red is going to close up a pentagon here. So once I have a few more pieces ready. I'll end up doing both this vertex and then immediately doing that vertex afterward. Okay, so I haven't actually put any of these junctions together over here. This is how it's going to go to make my first closed loop my first pentagon here. And so when I put these together, I will actually close into a pentagon here and will start to actually get some curvature some structure to this piece. You can see these pyramids don't quite line up because well they can't and stay planar. So actually this is going to start to force it to curve. And then I don't know if it's worth bringing people in, if there are people out in breakout rooms worth bringing them in for this or not. I'm making an announcement that they can come back if they wish. If they wish. Yeah. Okay, sounds good. And there's a question about whether there's a permanent record of the instructions. There will be soon posted on studio infinity.org. I'll post this whole bill. I just didn't want to post it ahead of time. I just wanted to make sure that everyone is now back here. So, okay. Very good. So you can see this is the structure that I've built so far. I'm, I'm, I'm focusing on the red section. But when I create this red vertex over here and I'll just, you know, do this, what I think of as previewing. To, to complete a red vertex here. In that woven fashion. And then we'll get to be sort of second nature as you make more vertices. You can see I actually am going to want these two to come together to close a pentagon. So they're actually going to tip like that. Now it feels a little uncomfortable, but that's because it's the pentagons that are responsible for creating the curvature here. So it should feel a little uncomfortable. And it turns out the third one at this vertex is going to be a pink, which is going to end up weaving in just like this. So here's all the connections I'm going to make. And I'm going to go ahead and connect them up that way. And you'll see that it'll start to, you know, want to curve. So I'm going to start with the red vertex. So this is straightforward. Just like now done a whole bunch of times. Get the buckle through first. Okay. And the big tab. Okay. Now I want to complete this red vertex. Okay. And this over that. So I get this over that. Tab out here. There we go. Here's the tab. And it's coming out and popping back in. Good. And the big tab. Okay. Now I've completed that red vertex. And one of the reasons I like this unit so much is that it makes the, the underlying graph. So I'm going to go ahead and do that. And I'm going to go ahead and do the vertices and edges of the polyhedron. You know, so clear here are the vertices and you can see the edge connections. And so looking at my diagram, I'm going to need to connect these that should be at the same vertex. So I'll go ahead and do that. Looks like I forgot to separate this tab. That's always a pain. When you're in the middle of putting together and you have to pop your tab out. Okay. There we go. And the big tab. Okay. And now I'll put in the third. I'll put in the third. Piece of this vertex. It's going to go. This in the end, and it's going to feel uncomfortable. That's going to feel like, did these really go together? Because again, we're creating. That curvature there. And so the stiff plastic is resisting that curvature, but we will beat it into submission. I've got the green where I want it. I'll get this buckle. Like so, like so. There we go. And one last big tab. And there we go. There's a first pentagon. First closed loop. And you can feel that there's some tension on this. And ultimately we're going to, it's going to end up being forced to curve out like this. Once we have more of the structure. So now I'm just going to continue along. And as I, you know, complete loops. Close them up like that. So that's what I had at this moment. I'm just going to go back to finishing off my red section. And then. Then I'll probably do the pink section next because I've already got two. Of the edges on it. All right, thanks. Hopefully, hopefully things are going well for you. If they're not, if you need any help or advice, just, just holler on the chat. So I had a quick question related to. Kind of instructions and other documentation. Suppose we wanted to run a similar activity for like a math circle or something. And we had access to, you know, a similar sort of. She cutter. Would you be able to make some of kind of like the templates or other things available so that. Yes, absolutely. So. There's a PDF already for cutting out a paper, but if you want to run it on. Actual cutting machine. Well, most of the consumer cutters you want an SVG file. So I will. Right after. Right after the event today, I'll post on discord. The exact cut file that I used to make these. And then within a. Well, let's say by next Wednesday. I'll have full instructions up on studio infinity.org. Awesome. Thanks. No problem. And it's all creative commons license. So everybody should feel absolutely free to. You know, copy, disseminate riff on this. As you like. I should say the, this is inspired by. An origami unit. That was created by a person by the name of Tom Hall. Obviously the single sheet cut out is a bit different, but the original fizz unit. Was invented. By Tom Hall. Glenn, someone in the chat asked how many colors total. Is being used if they want to follow along with you. I'm using five colors. One is the original fizz unit. I'm using five colors. One corresponding to each of the four faces of the original tetrahedron that the truncated triacus tetrahedron is based on. And a fifth color, which is for the edges of the original tetrahedron. What's what remains of the edges of the original tetrahedron. And that's nine pieces of each of the. Colors that correspond to the faces. And then six pieces because there's six edges of the, of the fifth color. Okay. And for those of you that happened to be in this room, I've now completed the entire red section. So this is what's left of one face. Of the original tetrahedron. Here's a green edge leading to now the pink face. So next I'm going to focus on finishing this pink face. I just have to step out briefly to get stuff set up for cutting for my workshop tomorrow. So I'll be back. Thank you. Thank you. Thank you. Thank you. Thank you. Edmund. You want to just check your chat. Yep. I just invited people back. Our folks back or. 10 seconds. Oh, okay. Very good. Oh, I like your shirt. Oh, yeah. It's sort of some designers attempt at maybe being a little inspired by Penrose rambuses. I don't know. I don't know. I don't know. I don't know. I don't know what styles pretty much are. I should probably switch back to, uh, yeah, I'll switch back to the main camera for me. Cause I can just hold up what I'm doing. Everyone is back now. Okay. Terrific. Well, I want to thank you all for participating, of course. And let's see where things stand. And the way I can get a kind of a reading on the chaos meter. So what I've got so far as I completed the red face and the white face, I've got to start with the first one. I'm going to start with the magenta face. So I'm over half done. Uh, maybe not quite two thirds done. Um, so, uh, and of course, I feel as well as various folks who are at different stages, uh, along the way. So I would rate this as a, uh, reduction, but not elimination in chaos. Um, and I do thank you for just being, I will stay here, uh, on, on this channel until I complete this. Um, I'm not sure how far it might be another 45 minutes or so. You're obviously have, uh, lots of things on your agendas and so on. So do not feel at all obliged to stay if you want to stay. Uh, and I think at this point, it's a smaller group. Uh, can, uh, you know, continue here in the main channel. We can even chat here in the main channel. Um, but, uh, you know, if you need to do other things, if you want to complete this on your own time, I'd love to see photos of what you build in the, uh, on Discord, there's a, there's a channel, uh, for this build. I will certainly post a picture of mine. Uh, and like I said, I will post all the cut files and so on. Uh, so that if you want to do similar things, you can and there'll be full, uh, instructions, directions on a suit infinity next week. Uh, I hope you've enjoyed what you've done so far. Like I said, if you want to keep building, don't let me stop you and I'll, I'll be continuing until I finish this, but thank you so much for participating. And I hope you're enjoying the week. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you, Glenn. This is terrific. Oh, good. I've got one more joint. One more. Oh, look at you. There you go. With the dodecahedron. Oh yes. The simplest one was the only one. I can, I gave myself any confidence. It is impressive. I get as well. It is impressively difficult to screw up. The only thing that I did wrong so far, or actually I finished. So the only thing I did wrong was I put four things together on one vertex and got a flat thing once. Yeah, yeah, yeah. But it is really impressively difficult to screw up I really recommend this. The tabs and slots kind of they align themselves is hopefully one of the advantages. And there's kind of only one thing to do, which is the right thing. Naturally, it very naturally sort of starts taking form. Yeah. Yeah, like the slots, like once you realize that that that thing is supposed to be a buckle and the other thing is supposed to be a slot. Everything only fits together in that one way. Right. So, I really appreciated that. That part worked. I'll also mention that I, I didn't get the pieces so I'm, I use the origami folded pieces that you linked to. But mine is very lopsided. That's one big advantage of the pieces you made is, even though I thought I was folding precisely to make the units. They must be different because they're right. My pentagons are kind of wonky. They can come out wonky with this because of differences in how crisply they're folded, but that is one advantage of the CNC is the uniformity of the resulting pieces. Exactly. Yeah. But it didn't take me it didn't take me too long. I'm not sure it's faster. Watching. Yeah, it's better. It is the pulling them apart from the matrix is unfortunately a little persnickety. And it would be nice to find a way in small quantities you can have the machine cut all the way through. And so literally you just get the separated pieces, but in large quantities on a roll you can't do that because the individual pieces can then get loose and jam up in the machine and and throw the entire production off. So for a large quantity you have to make them this way that they're like sort of, you know, pull apart as opposed to actually pre completely pre cut. What is the hardest part. Yeah, I also did my own origami pieces. And I think what Catherine was saying is true. There's like a propagation of error when you fold the pieces and just a little off. And then the whole figure is off. I think it's kind of like the same speed if you do it with the CNC pieces pieces and the paper pieces, although the paper ones. I think there's more like uncertainty on where things should fit. So maybe that also complicates the process. Yeah, I did it. The thing where you print it, and then cut it out and then I just used a razor blade on a like a cutting surface to cut them out. And it ended up almost completely symmetric. The only asymmetries are the paper I printed it on had varying thicknesses. Some of them did not like to go in certain slots because of that but other than that, like it was, it went very smoothly. So it, like the amount of time it took to cut them all out with the razor blade was excessive. Yeah, substantial. Yeah. But thank you for persevering. It was worth it. It's really nice. Yeah, yeah.