Watch this red cube somehow fit inside this blue shape

Originally published at:


this reminds me of the banach-tarski theorem.

1 Like

Not now, my head is still spinning from those damn spinning circles…

(fyi the url is one letter off from being clickable)

1 Like

I read the first part of the Wikipedia entry on that and concluded I could summarise it as: something impossible can be deemed possible if we make up a load of other stuff to ‘make’ it work. :wink:

The cube and the rhombic dodecahedron are related. Two cubes, each divided into six pieces from the center out to the vertices of the square faces, can be assembled to make one rhombic dodecahedron.

Over the years, I’ve made all 25 inter-relations of the five Platonic Solids ( and am now working on including the rhombic dodecahedron as well. So far I’ve built the tetrahedron inside the rhombic dodecahedron, the octahedron inside the rhombic dodeca, and the cube inside the rhombic dodeca. Still thinking about the icosahedron, pentagonal dodecahedron, and the rhombic dodecahedron inside the rhombic dodecahedron.

I also do an occasional free listserv on Geometry Links (contact me to get on the list) which is archived at

This topic was automatically closed after 5 days. New replies are no longer allowed.