Acronym ... Name 2huhoh+3tes+8co (?) Circumradius 1 Coordinates (1, 0, 0, 0)                & all permutations, all changes of sign (vertex inscribed 1/q-hex) (1/2, 1/2, 1/2, 1/2)   & all permutations, all changes of sign (vertex inscribed tes) or just   (1/sqrt(2), 1/sqrt(2), 0, 0)   & all permutations, all changes of sign (in dual ico positioning) General of army ico Colonel of regiment ico Confer non-Grünbaumian master: huhoh   tes

This Grünbaumian polychoron can be seen as a blend of 2 coincident huhoh (where the cho will blend out, while the thah would combine to 2thah) plus gico (the 3 tes compound) and 8 additional co cells. And indeed, the vertex figure is a crossed faceting of a rightangled-triangular prismatic half of the cube vertex figure of ico. Therefore the vertices of this polychoron coincide by 4.

Incidence matrix according to Dynkin symbol

```x3o3/2x4o

. .   . . | 96 |  2   4 |  1  4  2  2 |  2  2 1
----------+----+--------+-------------+--------
x .   . . |  2 | 96   * |  1  2  0  0 |  2  1 0
. .   x . |  2 |  * 192 |  0  1  1  1 |  1  1 1
----------+----+--------+-------------+--------
x3o   . . |  3 |  3   0 | 32  *  *  * |  2  0 0
x .   x . |  4 |  2   2 |  * 96  *  * |  1  1 0
. o3/2x . |  3 |  0   3 |  *  * 64  * |  1  0 1
. .   x4o |  4 |  0   4 |  *  *  * 48 |  0  1 1
----------+----+--------+-------------+--------
x3o3/2x . ♦ 12 | 12  12 |  4  6  4  0 | 16  * *
x .   x4o ♦  8 |  4   8 |  0  4  0  2 |  * 24 *
. o3/2x4o ♦ 12 |  0  24 |  0  0  8  6 |  *  * 8
```

```x3o3/2x4/3o

. .   .   . | 96 |  2   4 |  1  4  2  2 |  2  2 1
------------+----+--------+-------------+--------
x .   .   . |  2 | 96   * |  1  2  0  0 |  2  1 0
. .   x   . |  2 |  * 192 |  0  1  1  1 |  1  1 1
------------+----+--------+-------------+--------
x3o   .   . |  3 |  3   0 | 32  *  *  * |  2  0 0
x .   x   . |  4 |  2   2 |  * 96  *  * |  1  1 0
. o3/2x   . |  3 |  0   3 |  *  * 64  * |  1  0 1
. .   x4/3o |  4 |  0   4 |  *  *  * 48 |  0  1 1
------------+----+--------+-------------+--------
x3o3/2x   . ♦ 12 | 12  12 |  4  6  4  0 | 16  * *
x .   x4/3o ♦  8 |  4   8 |  0  4  0  2 |  * 24 *
. o3/2x4/3o ♦ 12 |  0  24 |  0  0  8  6 |  *  * 8
```

```x3/2o3x4o

.   . . . | 96 |  2   4 |  1  4  2  2 |  2  2 1
----------+----+--------+-------------+--------
x   . . . |  2 | 96   * |  1  2  0  0 |  2  1 0
.   . x . |  2 |  * 192 |  0  1  1  1 |  1  1 1
----------+----+--------+-------------+--------
x3/2o . . |  3 |  3   0 | 32  *  *  * |  2  0 0
x   . x . |  4 |  2   2 |  * 96  *  * |  1  1 0
.   o3x . |  3 |  0   3 |  *  * 64  * |  1  0 1
.   . x4o |  4 |  0   4 |  *  *  * 48 |  0  1 1
----------+----+--------+-------------+--------
x3/2o3x . ♦ 12 | 12  12 |  4  6  4  0 | 16  * *
x   . x4o ♦  8 |  4   8 |  0  4  0  2 |  * 24 *
.   o3x4o ♦ 12 |  0  24 |  0  0  8  6 |  *  * 8
```

```x3/2o3x4/3o

.   . .   . | 96 |  2   4 |  1  4  2  2 |  2  2 1
------------+----+--------+-------------+--------
x   . .   . |  2 | 96   * |  1  2  0  0 |  2  1 0
.   . x   . |  2 |  * 192 |  0  1  1  1 |  1  1 1
------------+----+--------+-------------+--------
x3/2o .   . |  3 |  3   0 | 32  *  *  * |  2  0 0
x   . x   . |  4 |  2   2 |  * 96  *  * |  1  1 0
.   o3x   . |  3 |  0   3 |  *  * 64  * |  1  0 1
.   . x4/3o |  4 |  0   4 |  *  *  * 48 |  0  1 1
------------+----+--------+-------------+--------
x3/2o3x   . ♦ 12 | 12  12 |  4  6  4  0 | 16  * *
x   . x4/3o ♦  8 |  4   8 |  0  4  0  2 |  * 24 *
.   o3x4/3o ♦ 12 |  0  24 |  0  0  8  6 |  *  * 8
```

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