cube compound v.f.
- Good thought, if I can draw that!
This article needs to illustrate the vertex figures to be intelligible. The current table has too many off-topic symbols which are not useful and serve only to draw focus away from the topic in hand. — Cheers, Steelpillow (Talk) 16:14, 9 June 2016 (UTC)
If we are calling them ditrigonal based on the presence of that word in their names (as opposed to the uncited current definition), then the other two have 60 vertices (not 20). Double sharp (talk) 10:10, 10 June 2016 (UTC)
- I cannot find a source for that definition, I have moved it to where it is more descriptive of certain figures - including the count of 20. BTW, I misread Har'el first time round but have now corrected that. — Cheers, Steelpillow (Talk) 10:34, 10 June 2016 (UTC)
A tiny handful of unreliable hits in Google, not a peep out of mathworld, so I removed them from the article. If anybody can find sufficient reliable sources per WP:RS then it might be possible to restore some of it, either here or in a polytope article. So here it is for now. — Cheers, Steelpillow (Talk) 12:40, 10 June 2016 (UTC)
Norman Johnson discovered three related antiprism-like star polytopes in 1966, now named the Johnson antiprisms. These have these ditrigonal star polyhedra as their bases. They all have 40 vertices, 40 total cells, and 180 total faces. They have 184 (small ditrigonal icosidodecahedral antiprism), 168 (ditrigonal dodecadodecahedral antiprism), and 184 (great ditrigonal icosidodecahedral antiprism) edges respectively. Their Coxeter-Dynkin diagrams are , , and respectively.<ref>Norman Johnson, ''The Theory of Uniform Polytopes and Honeycombs'', Ph.D. Dissertation, University of Toronto, 1966 [https://getinfo.de/app/The-theory-of-uniform-polytopes-and-honeycombs/id/TIBKAT%3A22693604X]</ref> 
- External links
- Category 20: Miscellaneous star polychora 966:Sidtidap, 967:ditdidap, and 968:gidtidap are commonly referred to as the Johnson Antiprisms, for they were discovered by Norman Johnson, they also form a regiment.
- Klitzing, Richard. "Uniform star polychoron 966 small-ditrigonal-icosidodecahedron antiprism (sidtidap)".
- Klitzing, Richard. "Uniform star polychoron 967 ditrigonal-dodecadodecahedron antiprism (ditdidap)".
- Klitzing, Richard. "Uniform star polychoron 968 great-ditrigonal-icosidodecahedron antiprism (gidtidap)".