Incomplete Open Platonic Solids
2026/02/23 by Mikael Vejdemo-Johansson · 3 voices
Mathematics · Computer Science · #math.CO #cs.CG
paper · pdf
Abstract
Sol LeWitt famously enumerated all the incomplete open cubes, finding 122 of these connected, non-planar subsets of the edges of the cube. Since then, while several projects have revisited the cube enumeration, no such enumeration has been published for any other interesting solid. In this paper we present work on enumerating all the incomplete open platonic solids, finding 6 tetrahedra, 122 cubes (just like LeWitt), 185 octahedra, 2 423 206 dodecahedra and 16 096 166 icosahedra.
Discussions
- Found it: arxiv.org/abs/2602.20425 [bsky, 4 points, 1 comments]
- “In this paper we present work on enumerating all the incomplete open platonic solids, finding 6 tetrahedra, 122 cubes (just like LeWitt), 185 octahedra, 2,423,206 dodecahedra and 16,096,166 icosahedr [bsky, 1 points, 2 comments]
- New preprint dropped: arxiv.org/abs/2602.20425 In addition to Sol LeWitt's 122 incomplete open cubes, there are 6 incomplete open tetrahedra, 185 incomplete open octahedra, 2423206 incomplete open dod [bsky, 0 points, 0 comments]
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