Acronym ...
Name 2hehad (?)
Circumradius 1/sqrt(2) = 0.707107
Coordinates (1/sqrt(2), 0, 0, 0, 0)   & all permutations, all changes of sign
General of army tac
Colonel of regiment tac
Confer
non-Grünbaumian master:
hehad  

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


Incidence matrix according to Dynkin symbol

x3o3o3o3/2o3*b

. . . .   .    | 10   8 |  48 | 32 32 |  8  8  8
---------------+----+----+-----+-------+---------
x . . .   .    |  2 | 40   12 | 12 12 |  4  6  4
---------------+----+----+-----+-------+---------
x3o . .   .    |  3 |  3 | 160 |  2  2 |  1  2  1
---------------+----+----+-----+-------+---------
x3o3o .   .      4 |  6 |   4 | 80  * |  1  1  0
x3o . .   o3*b   4 |  6 |   4 |  * 80 |  0  1  1
---------------+----+----+-----+-------+---------
x3o3o3o   .      5 | 10 |  10 |  5  0 | 16  *  *
x3o3o .   o3*b   8 | 24 |  32 |  8  8 |  * 10  *
x3o . o3/2o3*b   5 | 10 |  10 |  0  5 |  *  * 16

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