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
non-Grünbaumian master:
rico  
Grünbaumian relatives:
2rico   2rico+64{6}+128{3}  

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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