Acronym ... Name 2gohi (?) Circumradius (1+sqrt(5))/2 = 1.618034 Inradius (3+sqrt(5))/4 = 1.309017 Coordinates (τ, 0, 0, 0)             & all permutations, all changes of sign (vertex inscribed f/q-hex) (τ/2, τ/2, τ/2, τ/2)   & all permutations, all changes of sign (vertex inscribed f-tes) (τ2/2, τ/2, 1/2, 0)   & even permutations, all changes of sign (vertex inscribed sadi) where τ = (1+sqrt(5))/2 (a. and b. together define a vertex inscribed f-ico) General of army ex Colonel of regiment ex Confer non-Grünbaumian master: gohi   Grünbaumian relatives: ex+gohi+120id

Looks like a compound of 2 gohi with vertices and edges identified, while faces and cells coincide by pairs.

As abstract polytope 2gohi is isomorphic to 2gashi, thereby replacing gad by sissid, resp. replacing pentagonal faces by pentagrammal ones, resp. replacing 2sissid vertex figures by 2gad ones.

Incidence matrix according to Dynkin symbol

```x5o5/2o5/2o5/2*b

. .   .   .      | 120 ♦  12 |   60 |  12  12
-----------------+-----+-----+------+--------
x .   .   .      |   2 | 720 |   10 |   5   5
-----------------+-----+-----+------+--------
x5o   .   .      |   5 |   5 | 1440 |   1   1
-----------------+-----+-----+------+--------
x5o5/2o   .      ♦  12 |  30 |   12 | 120   *
x5o   .   o5/2*b ♦  12 |  30 |   12 |   * 120

or
. .   .   .         | 120 ♦  12 |   60 |  24
--------------------+-----+-----+------+----
x .   .   .         |   2 | 720 |   10 |  10
--------------------+-----+-----+------+----
x5o   .   .         |   5 |   5 | 1440 |   2
--------------------+-----+-----+------+----
x5o5/2o   .       & ♦  12 |  30 |   12 | 240
```

```x5o5/2o5/3o5/3*b

. .   .   .      | 120 ♦  12 |   60 |  12  12
-----------------+-----+-----+------+--------
x .   .   .      |   2 | 720 |   10 |   5   5
-----------------+-----+-----+------+--------
x5o   .   .      |   5 |   5 | 1440 |   1   1
-----------------+-----+-----+------+--------
x5o5/2o   .      ♦  12 |  30 |   12 | 120   *
x5o   .   o5/3*b ♦  12 |  30 |   12 |   * 120
```

```x5o5/3o5/2o5/3*b

. .   .   .      | 120 ♦  12 |   60 |  12  12
-----------------+-----+-----+------+--------
x .   .   .      |   2 | 720 |   10 |   5   5
-----------------+-----+-----+------+--------
x5o   .   .      |   5 |   5 | 1440 |   1   1
-----------------+-----+-----+------+--------
x5o5/3o   .      ♦  12 |  30 |   12 | 120   *
x5o   .   o5/3*b ♦  12 |  30 |   12 |   * 120

or
. .   .   .         | 120 ♦  12 |   60 |  24
--------------------+-----+-----+------+----
x .   .   .         |   2 | 720 |   10 |  10
--------------------+-----+-----+------+----
x5o   .   .         |   5 |   5 | 1440 |   2
--------------------+-----+-----+------+----
x5o5/3o   .       & ♦  12 |  30 |   12 | 240
```

```x5/4o5/2o5/2o5/2*b

.   .   .   .      | 120 ♦  12 |   60 |  12  12
-------------------+-----+-----+------+--------
x   .   .   .      |   2 | 720 |   10 |   5   5
-------------------+-----+-----+------+--------
x5/4o   .   .      |   5 |   5 | 1440 |   1   1
-------------------+-----+-----+------+--------
x5/4o5/2o   .      ♦  12 |  30 |   12 | 120   *
x5/4o   .   o5/2*b ♦  12 |  30 |   12 |   * 120

or
.   .   .   .         | 120 ♦  12 |   60 |  24
----------------------+-----+-----+------+----
x   .   .   .         |   2 | 720 |   10 |  10
----------------------+-----+-----+------+----
x5/4o   .   .         |   5 |   5 | 1440 |   2
----------------------+-----+-----+------+----
x5/4o5/2o   .       & ♦  12 |  30 |   12 | 240
```

```x5/4o5/2o5/3o5/3*b

.   .   .   .      | 120 ♦  12 |   60 |  12  12
-------------------+-----+-----+------+--------
x   .   .   .      |   2 | 720 |   10 |   5   5
-------------------+-----+-----+------+--------
x5/4o   .   .      |   5 |   5 | 1440 |   1   1
-------------------+-----+-----+------+--------
x5/4o5/2o   .      ♦  12 |  30 |   12 | 120   *
x5/4o   .   o5/3*b ♦  12 |  30 |   12 |   * 120
```

```x5/4o5/3o5/2o5/3*b

.   .   .   .      | 120 ♦  12 |   60 |  12  12
-------------------+-----+-----+------+--------
x   .   .   .      |   2 | 720 |   10 |   5   5
-------------------+-----+-----+------+--------
x5/4o   .   .      |   5 |   5 | 1440 |   1   1
-------------------+-----+-----+------+--------
x5/4o5/3o   .      ♦  12 |  30 |   12 | 120   *
x5/4o   .   o5/3*b ♦  12 |  30 |   12 |   * 120

or
.   .   .   .         | 120 ♦  12 |   60 |  24
----------------------+-----+-----+------+----
x   .   .   .         |   2 | 720 |   10 |  10
----------------------+-----+-----+------+----
x5/4o   .   .         |   5 |   5 | 1440 |   2
----------------------+-----+-----+------+----
x5/4o5/3o   .       & ♦  12 |  30 |   12 | 240
```