26 Polyhedra that Fit Through Themselves, and 5 that Might Not

3D animation showing the Rupert Property for 26 polyhedra: all 5 Platonic solids (including "Prince Rupert's Cube"), 11 out of the 13 Catalan solids, and 10 out of the 13 Archimedean solids.

Thank you to ‪@tom7‬ for the solver code. See http://tom7.org/ruperts/ for more information.

The music is available on Bandcamp: https://dwrensha.bandcamp.com/album/r...

Presented at SIGBOVIK 2025.

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Rupert's Roundup

00:00 - tetrahedron
00:08 - cube
00:16 - octahedron
00:24 - dodecahedron
00:32 - icosahedron
00:40 - tetrakis hexahedron
00:48 - truncated octahedron
00:56 - triakis octahedron
01:04 - truncated cube
01:12 - pentakis dodecahedron
01:20 - truncated icosahedron
01:28 - triakis icosahedron
01:36 - truncated dodecahedron
01:44 - rhombic dodecahedron
01:52 - cuboctahedron
02:00 - rhombic triacontahedron
02:08 - icosidodecahedron
02:16 - disdyakis dodecahedron
02:24 - truncated cuboctahedron
02:32 - disdyakis triacontahedron
02:40 - truncated icosidodecahedron
02:48 - deltoidal icositetrahedron
02:56 - rhombicuboctahedron
03:04 - triakis tetrahedron
03:12 - truncated tetrahedron
03:20 - pentagonal icositetrahedron
03:28 - snub cube
03:32 - pentagonal hexecontahedron
03:36 - snub dodecahedron
03:40 - deltoidal hexecontahedron
03:44 - rhombicosidodecahedron
03:48 - the full lineup