The Happier Cube! (Hyper-Cube variation)

http://www.24cell.net This is the much Hyped Happier Hyper Cube (can you say this ten times?), which can change its dazzling colors when going inside out. The goal is to exchange the outside blue cube with the inside red cube, and vice versa!

It is based on a 3D projection of the HyperCube (aka Tesseract) and it uses four dimensional symmetry to exchange the edges.

It is not as rigid as the Hyperion (the other HyperCube variant that I made), so it is easier to manipulate it. However, adjusting and calibrating can take some time!!! The video was taken at the headquarters of the Mechanical & Mathematical Puzzle Club. :-)

Category:

Education

Tags:

• 4D
• fourth dimension
• four dimensionsal
• flatland
• flatliners
• symmerty
• pentachoron
• Chronos
• time-space
• 24-cell
• tesseract
• hypercube
• 16-cell
• Pantazis Houlis
• Cubedron
• Aquadron
• Puzzle Ninja
• MindStrat

[heiowge]

The orange and blue cubes both have 12 edges, but there are 8 green connectors to make the vertices meet.  Where are the other 4 going?

[kastellorizo]

@heiowge That's it! There are 32 edges in total! :-)

[heiowge]

@kastellorizo Correct me if I'm wrong, but isn't a hypercube where they cycle 3 ways rather than swap 2 sets? That would necessitate 12 of each. Or am I being rude?

Either way, it's a hell of an accomplishment.

[kastellorizo]

@heiowge no you aren't being rude, I am always happy to explain! :-)

The Hypercube has 16 vertices and 32 edges by definition. It also has 8 cube-cells, which is why it is called 8-cell. It is vertex & edge transitive, so any edge may be swapped with any other edge. You could surely have all eight green edges to be contained inside a cube, but there will always be edges of the other colors too. It would be nice if it had 36 edges so that I can have three cubes of different color, but it doesn't!

[Falcrist]

Please remake this video at a better angle. I can't see anything past your right hand. :(

[thepanzer1]

i dont know about you guys but i cant seem to see ANYTHING THATS GOING ON. your hands are kind of in the way. haha still seems kind of puzzling. =)

[kastellorizo]

@ruberciubeing Yes I know the movie, and you can re-live it with this puzzle, for REAL! :-P

[SaiyanKirby]

@ruberciubeing

The horror/thriller/whatever?

[carpenoctem66]

That looks endlessly entertaining.