| Acronym | ... |
| Name | 2rico+64{6}+192{3} (?) |
| Circumradius | sqrt(3) = 1.732051 |
| Coordinates | (sqrt(2), 1/sqrt(2), 1/sqrt(2), 0) & all permutations, all changes of sign |
| General of army | rico |
| Colonel of regiment | rico |
| Confer |
|
This is a scaliform variant of a faceting of a Grünbaumian double-cover of the prismatorhombated hexadecachoron (proh). It comes out to be edge-inscribable to the rectified icositetrachoron (rico). The additional 64 hexagons are the diametrals of 2 tesseractic subgroups of the former cuboctahedra (co), the additional 192 triangles are used to produce an octuple coincidence of the former co-co triangles where both belong to that subgroup.
Incidence matrix according to Dynkin symbol
β3o3x4β
both( . . . . ) | 192 | 2 2 2 2 | 1 1 2 2 3 4 1 | 1 1 2 1 3
----------------+-----+-----------------+------------------------+---------------
both( . . x . ) | 2 | 192 2 * * | 1 0 1 1 0 1 0 | 1 0 1 1 1
both( s .2. s ) | 2 | * 192 * * | 0 0 0 0 2 2 0 | 0 1 1 0 2
sefa( β3o . . ) | 2 | * * 192 * | 0 1 0 1 1 0 0 | 1 1 0 0 1
sefa( . . x4s ) | 2 | * * * 192 | 0 0 1 0 0 1 1 | 0 0 1 1 1
----------------+-----+-----------------+------------------------+---------------
both( . o3x . ) | 3 | 3 0 0 0 | 64 * * * * * * | 1 0 0 1 0
β3o . . ♦ 3 | 0 0 3 0 | * 64 * * * * * | 1 1 0 0 0
both( . . x4s ) ♦ 4 | 2 0 0 2 | * * 96 * * * * | 0 0 1 1 0
sefa( β3o3x . ) | 6 | 3 0 3 0 | * * * 64 * * * | 1 0 0 0 1
sefa( β3o 2 β ) | 3 | 0 2 1 0 | * * * * 192 * * | 0 1 0 0 1
sefa( s 2 x4s ) | 4 | 1 2 0 1 | * * * * * 192 * | 0 0 1 0 1
sefa( . o3x4s ) | 3 | 0 0 0 3 | * * * * * * 64 | 0 0 0 1 1
----------------+-----+-----------------+------------------------+---------------
β3o3x . ♦ 12 | 12 0 12 0 | 4 4 0 4 0 0 0 | 16 * * * *
β3o 2 β ♦ 6 | 0 6 6 0 | 0 2 0 0 6 0 0 | * 32 * * *
both( s 2 x4s ) ♦ 8 | 4 4 0 4 | 0 0 2 0 0 4 0 | * * 48 * *
both( . o3x4s ) ♦ 12 | 12 0 0 12 | 4 0 6 0 0 0 4 | * * * 16 *
sefa( β3o3x4β ) ♦ 9 | 3 6 3 3 | 0 0 0 1 3 3 1 | * * * * 64
starting figure: x3o3x4x
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