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

```x3o3o3o3o3/2*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 . . o3/2*b ♦  4 |  6 |   4 |  * 80 |  0  1  1
---------------+----+----+-----+-------+---------
x3o3o3o .      ♦  5 | 10 |  10 |  5  0 | 16  *  *
x3o3o . o3/2*b ♦  8 | 24 |  32 |  8  8 |  * 10  *
x3o . o3o3/2*b ♦  5 | 10 |  10 |  0  5 |  *  * 16
```

```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
```