Amazing at 3:50 I am a math teacher and I didn't know that. It's kind of funny they are duals and self duals. You think they would all be connected in one Geometric way. I also find it fascinating we find them so aesthetically pleasing.
LOL at the song! When he was imaginary?
My fav is the tetra always has been, but I like the isodeca also. Close second. I was never a fan of the 8 sided variety...something about the square in the middle bugs me. It feels like cheating...like a 10 sided dice.
It is really interesting to learn which shapes are dual to which and which are self dual. They are connected in one grand way, though. The more I learn about polyhedra, the more I see this. The dodecahedron, for example, is in many ways just a weird cube.
The octahedron is very much a "square" shape. The square pops up just as much in an octahedron as a triangle does in a cube. (or example, the vertex pattern).
very useful thanks, but just wondering if you know what the minimum number of colours that would be needed to systematically colour the five platonic solids, with the rule that 2 faces with a common edge can't be the same colour. trying to revise for exam, can sort of work it out but want to make sure?
As far as I know there should be a minimum of four colors necessary.. I don't know too much about it, but my understanding is that the four color theorem applies to spherical surfaces (which would mean it applies to the Platonic solids.)
As a side note, The octahedron is unique in that it is the only one that can be colored with two alternating colors (like a checker board).
Hope that helps. Let me know if I got something wrong!
Even without this, there are many possibly ways to work out the geometry of space. Theoreticly an infinite number of dimentions can be worked with, a trillion a Googol, Centillion tetrated to a Centillion tetrated to a Centillion to 10^303^10^303 levels, a vast amount of algorithms can be made. Geometry has many ecciting possibilities that reach beyond it's self.
Thanks for the thought! I have a video on other geometric shapes as well. I think that in some way there must be an infinity of dimensions. As it turns out, though, beyond 4d, all dimensions only have 3 regular solids- the simplex, the hypercube, and it's dual the orthoplex.
What could be learned with 27 shapes or three axis of shapes, there may need to be a symbol to represent of number of shape axis, this may in face make a large shape in it's self a cube of three axis or 27 shapes, does this trail into another level of shape representation? This has untold implications for gauging the geometry of space even in a basic area like this there are fundemental discoveries to be made.
I'm not saying these are the Platonic solids but you could even made a space equation for shapes in general if you were creative enough. Maybe examine the ratio between these nine shapes, the triangle, the square, the pentagon, the tetrahedron, the cube, the dodecahedron, a 4 dimentional tetrahedron, the tesseract or 4 dimentional cube and the 4 dimentional dodecahedron. This however is just 9 shapes or two axis of shapes.
The painting "Harmony" by the Spanish/Mexican artist, Ramidios Varo, features the Platonic solids as auxillary elements in a composition about, of all things, imaginary numbers. I haven't been able to find an imagine on the web showing the canvass in enough detail to make all of this out.
Is it sad that when i think of polyhedra, I can't help but see D & D dice?
Is there a computer programe or something that can plot shapes if you input the number of edges, vertexs and faces, that'd be sooo cool :D
You don't need a practical purpose of things this amazing. Aren't they used in computer graphics and physics a lot /is ignorant/ definitely useful in chemistry and minerology
I came to this video after watching the Galactic Confederation of Light Teachings... I am not a geometric (or what people who study sacred geometry are called), so all of the below comments are like reading Hebrew, pardon my ignorance. However, I find it fascinating these platonics are what construct us and everything in or universe. i was waiting for you to turn the whatever the triangle one's called (sorry) into the merkaba...that I am familiar with!
not sure what you mean, though.. imaginary faces? Do you mean, like a 3.14 sided polygon or something? I really don't know, but I think it's worth exploring. Maybe fractals would come into play somehow (having fractional dimensions), but I think that would make them concave.
I have an absurd thought. Can we just take numbers, whose negation equals two, and force the faces and vertices into convex polyhedra? Do we need imaginary faces to do this with numbers outside of the platonics?
I found some info on which numbers work and which do not for Euler's polyhedron formula. For example, did you know that you cannot have a a polyhedron with 7 edges?
Also, there is a similar formula for tilings, just replace the 2 with a 1!
I want to start a geometry company. Begin with some games, move on to good tools for making these. I have specific requirements for the plastics involved. Wish we could get some money together and work together...
I'd like to get involved. Maybe we could get in touch with someone already working on geometry stuff or games or toys so we don't have to start from scratch.
I'm friends with a guy who works for zometool, but I've had a hard time contacting him.
@AdamLore Hey, do you know that the reg. tetrahedron is the only solid made up of the longest of edges there are no longer lines through its face or body diagonal as it is true for all the other solids, I think this also applies to all the polygons where simmilar aplies to the equilateral triangle. All other solids or polygons contain longer edges throuhg the face or body diagonals.
thank you for sharing. =)
CovenantOfLove 1 month ago
triangle is self dual :)
chriswilliamstool 1 month ago
Amazing at 3:50 I am a math teacher and I didn't know that. It's kind of funny they are duals and self duals. You think they would all be connected in one Geometric way. I also find it fascinating we find them so aesthetically pleasing.
LOL at the song! When he was imaginary?
My fav is the tetra always has been, but I like the isodeca also. Close second. I was never a fan of the 8 sided variety...something about the square in the middle bugs me. It feels like cheating...like a 10 sided dice.
CMrace 8 months ago
@CMrace
It is really interesting to learn which shapes are dual to which and which are self dual. They are connected in one grand way, though. The more I learn about polyhedra, the more I see this. The dodecahedron, for example, is in many ways just a weird cube.
The octahedron is very much a "square" shape. The square pops up just as much in an octahedron as a triangle does in a cube. (or example, the vertex pattern).
Thanks for your comments!
AdamLore 8 months ago
i was in class when my teacher started playing this video, and there as quite a.... reaction from the song :D
Mobrun2121 9 months ago 3
@Mobrun2121
That is really funny!
AdamLore 9 months ago
very useful thanks, but just wondering if you know what the minimum number of colours that would be needed to systematically colour the five platonic solids, with the rule that 2 faces with a common edge can't be the same colour. trying to revise for exam, can sort of work it out but want to make sure?
hannahtiz 9 months ago
@hannahtiz
As far as I know there should be a minimum of four colors necessary.. I don't know too much about it, but my understanding is that the four color theorem applies to spherical surfaces (which would mean it applies to the Platonic solids.)
As a side note, The octahedron is unique in that it is the only one that can be colored with two alternating colors (like a checker board).
Hope that helps. Let me know if I got something wrong!
AdamLore 9 months ago
Even without this, there are many possibly ways to work out the geometry of space. Theoreticly an infinite number of dimentions can be worked with, a trillion a Googol, Centillion tetrated to a Centillion tetrated to a Centillion to 10^303^10^303 levels, a vast amount of algorithms can be made. Geometry has many ecciting possibilities that reach beyond it's self.
RJL738 10 months ago
@RJL738
Thanks for the thought! I have a video on other geometric shapes as well. I think that in some way there must be an infinity of dimensions. As it turns out, though, beyond 4d, all dimensions only have 3 regular solids- the simplex, the hypercube, and it's dual the orthoplex.
AdamLore 10 months ago
@AdamLore Fair enough but yes the posibilities are wonderful.
RJL738 10 months ago
What could be learned with 27 shapes or three axis of shapes, there may need to be a symbol to represent of number of shape axis, this may in face make a large shape in it's self a cube of three axis or 27 shapes, does this trail into another level of shape representation? This has untold implications for gauging the geometry of space even in a basic area like this there are fundemental discoveries to be made.
RJL738 10 months ago
I'm not saying these are the Platonic solids but you could even made a space equation for shapes in general if you were creative enough. Maybe examine the ratio between these nine shapes, the triangle, the square, the pentagon, the tetrahedron, the cube, the dodecahedron, a 4 dimentional tetrahedron, the tesseract or 4 dimentional cube and the 4 dimentional dodecahedron. This however is just 9 shapes or two axis of shapes.
RJL738 10 months ago
THAT SONG IS WAAAAAYYYYY TOO FUNNY HAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHA
when i was the square root of a negative number
sanguinesurfer 10 months ago
The painting "Harmony" by the Spanish/Mexican artist, Ramidios Varo, features the Platonic solids as auxillary elements in a composition about, of all things, imaginary numbers. I haven't been able to find an imagine on the web showing the canvass in enough detail to make all of this out.
victor7574 10 months ago
@victor7574
Thanks Victor! I love Varo's work, didn't know she had the Platonic solids in any of her paintings.
AdamLore 10 months ago
stop the music!!1
sonofhendrix 1 year ago
"...we would have sexual intercourse, but at the same time, we would not have sexual intercorse..."
lol gotta love quantum physics. Awesome video. :)
Ant42Lee 1 year ago
@Ant42Lee
Good stuff. Thanks for watching. :-)
AdamLore 1 year ago
only shape missing from platonic is Pi*4 and its so common that its known as universal constant
another irony is the divisions of Pi give the triangle quad and pentagon used to construct them
okuma0kuma 1 year ago
Jack and Annie from Frog Creek, PA came to Florence,Italy to help Leonardo da Vinci.
Griffinsdad3401 1 year ago
lol...boxes
TheUFOeffect 1 year ago
cool video
bornkool 1 year ago
LOL at "and others" at 5:43. Mystery Artist makes old Leo look like a hack!
GlorifiedTruth 1 year ago
@GlorifiedTruth
It's my painting. lol.
AdamLore 1 year ago
Love this video. Lucid and elegant. Great work.
Albert Carpenter
MrAlbertpcarpenter 2 years ago
Thanks a lot, MrAlbert.
Be sure to check out the Archimedean Solids video if you are interested, and look forward to a new Catalan Solids video coming soon!
AdamLore 2 years ago
Is it sad that when i think of polyhedra, I can't help but see D & D dice?
Is there a computer programe or something that can plot shapes if you input the number of edges, vertexs and faces, that'd be sooo cool :D
You don't need a practical purpose of things this amazing. Aren't they used in computer graphics and physics a lot /is ignorant/ definitely useful in chemistry and minerology
unassumption 2 years ago
@unassumption yes, there is, try this website mathematik.uni-bielefeld.de/~CaGe/triangulations.html
gothaar 1 year ago
I came to this video after watching the Galactic Confederation of Light Teachings... I am not a geometric (or what people who study sacred geometry are called), so all of the below comments are like reading Hebrew, pardon my ignorance. However, I find it fascinating these platonics are what construct us and everything in or universe. i was waiting for you to turn the whatever the triangle one's called (sorry) into the merkaba...that I am familiar with!
therealjordanblue 2 years ago
Great video!
birdyhop1 2 years ago
gracias.
AdamLore 2 years ago
Holy crap this is a great video. I spent much of 8th grade with my friend Mark trying to discover a 6th perfect solid. :-)
My bad.
SaganAppreciationSoc 2 years ago
Thank you!
Did you guys come up with any cool new shapes?
AdamLore 2 years ago
If we had, you'd know our names by now. :-)
SaganAppreciationSoc 2 years ago
Thanks, V..
not sure what you mean, though.. imaginary faces? Do you mean, like a 3.14 sided polygon or something? I really don't know, but I think it's worth exploring. Maybe fractals would come into play somehow (having fractional dimensions), but I think that would make them concave.
AdamLore 2 years ago
I have an absurd thought. Can we just take numbers, whose negation equals two, and force the faces and vertices into convex polyhedra? Do we need imaginary faces to do this with numbers outside of the platonics?
This was a real masterpiece video, man.
AtheistHQ 2 years ago
I found some info on which numbers work and which do not for Euler's polyhedron formula. For example, did you know that you cannot have a a polyhedron with 7 edges?
Also, there is a similar formula for tilings, just replace the 2 with a 1!
AdamLore 2 years ago
Good work, Adam.
I want to start a geometry company. Begin with some games, move on to good tools for making these. I have specific requirements for the plastics involved. Wish we could get some money together and work together...
AtheistHQ 2 years ago
I'd like to get involved. Maybe we could get in touch with someone already working on geometry stuff or games or toys so we don't have to start from scratch.
I'm friends with a guy who works for zometool, but I've had a hard time contacting him.
AdamLore 2 years ago
@AdamLore
Contact me I already have what we need
frank
ElusiveCube 2 years ago
@AdamLore Hey, do you know that the reg. tetrahedron is the only solid made up of the longest of edges there are no longer lines through its face or body diagonal as it is true for all the other solids, I think this also applies to all the polygons where simmilar aplies to the equilateral triangle. All other solids or polygons contain longer edges throuhg the face or body diagonals.
polyhedron F+V-E =2 and a polygon F+V-E=1
frank
ElusiveCube 2 years ago