Acronym ...
Name 2rhohid (?)
Circumradius 1
Coordinates (1/sqrt(2), 1/sqrt(2), 0, 0, 0)   & all permutations, all changes of sign
General of army rat
Colonel of regiment rat
Confer
non-Grünbaumian master:
rhohid  

This Grünbaumian polyteron indeed has all elements in coincident pairs, only the vertices are identified; thus the vertex figure becomes a Grünbaumian double-cover of thahp.


Incidence matrix according to Dynkin symbol

o3x3o3o3/2o3*b

. . . .   .    | 40   24 |  12  24  24 | 12 12  8 12  8 |  4  6  4  2
---------------+----+-----+-------------+----------------+------------
. x . .   .    |  2 | 480 |   1   2   2 |  2  2  1  2  1 |  1  2  1  1
---------------+----+-----+-------------+----------------+------------
o3x . .   .    |  3 |   3 | 160   *   * |  2  2  0  0  0 |  1  2  1  0
. x3o .   .    |  3 |   3 |   * 320   * |  1  0  1  1  0 |  1  1  0  1
. x . .   o3*b |  3 |   3 |   *   * 320 |  0  1  0  1  1 |  0  1  1  1
---------------+----+-----+-------------+----------------+------------
o3x3o .   .      6 |  12 |   4   4   0 | 80  *  *  *  * |  1  1  0  0
o3x . .   o3*b   6 |  12 |   4   0   4 |  * 80  *  *  * |  0  1  1  0
. x3o3o   .      4 |   6 |   0   4   0 |  *  * 80  *  * |  1  0  0  1
. x3o .   o3*b   6 |  12 |   0   4   4 |  *  *  * 80  * |  0  1  0  1
. x . o3/2o3*b   4 |   6 |   0   0   4 |  *  *  *  * 80 |  0  0  1  1
---------------+----+-----+-------------+----------------+------------
o3x3o3o   .     10 |  30 |  10  20   0 |  5  0  5  0  0 | 16  *  *  *
o3x3o .   o3*b  24 |  96 |  32  32  32 |  8  8  0  8  0 |  * 10  *  *
o3x . o3/2o3*b  10 |  30 |  10   0  20 |  0  5  0  0  5 |  *  * 16  *
. x3o3o3/2o3*b   8 |  48 |   0  32  32 |  0  0  8  8  8 |  *  *  * 10

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