Hooped-up 24-cell
The 24-cell is really cool. It’s the only self-dual regular polytope that’s not a simplex or a polygon. Its vertices form the multiplicative group of units in the Hurwitz quaternion ring. It tiles Euclidean 4-space. Spheres inscribed in the octahedra give the closest packing of spheres in 4 dimensions. And, well, there are 24 of them.
We ran out of tape while making the inner cuboctahedron–one of the triangular sides is missing. But we came darn close! Compare:
You make some amazing stuff Mike! Most especially your three little boys!
[...] lost Letter and P=NP (with the usual great amount of useful comments), glanced at the very cool (almost complete) 24-cell on reperiendi, enjoyed Har-har-Hardy jokes and the bucket list new year’s resolutions at Math [...]
So what exactly do you tell your boys that you are making with the hoops? What do an 8 and 5 year old understand this cool thing to be?
The younger ones just enjoyed making it and didn’t care at all that it was a 3d projection of a 4d shape. Aidan would at least listen to me explain what it was.