Acronym ... Name 2fix (?) 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: fix   Grünbaumian relatives: fix+gahi+120id

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

As abstract polytope 2fix is isomorphic to 2gofix, thereby replacing ike by gike, resp. replacing pentagrammal edge figures by pentagonal ones, resp. replacing 2gad vertex figures by 2sissid ones.

Incidence matrix according to Dynkin symbol

```x3o5o5o5/4*b

. . . .      | 120 ♦  12 |   60 |  12  12
-------------+-----+-----+------+--------
x . . .      |   2 | 720 |   10 |   5   5
-------------+-----+-----+------+--------
x3o . .      |   3 |   3 | 2400 |   1   1
-------------+-----+-----+------+--------
x3o5o .      ♦  12 |  30 |   20 | 120   *
x3o . o5/4*b ♦  12 |  30 |   20 |   * 120
```

```x3o5o5/4o5*b

. . .   .    | 120 ♦  12 |   60 |  12  12
-------------+-----+-----+------+--------
x . .   .    |   2 | 720 |   10 |   5   5
-------------+-----+-----+------+--------
x3o .   .    |   3 |   3 | 2400 |   1   1
-------------+-----+-----+------+--------
x3o5o   .    ♦  12 |  30 |   20 | 120   *
x3o .   o5*b ♦  12 |  30 |   20 |   * 120
```
```or
. . .   .       | 120 ♦  12 |   60 |  24
----------------+-----+-----+------+----
x . .   .       |   2 | 720 |   10 |  10
----------------+-----+-----+------+----
x3o .   .       |   3 |   3 | 2400 |   2
----------------+-----+-----+------+----
x3o5o   .     & ♦  12 |  30 |   20 | 240
```

```x3o5/4o5/4o5/4*b

. .   .   .      | 120 ♦  12 |   60 |  12  12
-----------------+-----+-----+------+--------
x .   .   .      |   2 | 720 |   10 |   5   5
-----------------+-----+-----+------+--------
x3o   .   .      |   3 |   3 | 2400 |   1   1
-----------------+-----+-----+------+--------
x3o5/4o   .      ♦  12 |  30 |   20 | 120   *
x3o   .   o5/4*b ♦  12 |  30 |   20 |   * 120
```
```or
. .   .   .         | 120 ♦  12 |   60 |  24
--------------------+-----+-----+------+----
x .   .   .         |   2 | 720 |   10 |  10
--------------------+-----+-----+------+----
x3o   .   .         |   3 |   3 | 2400 |   2
--------------------+-----+-----+------+----
x3o5/4o   .       & ♦  12 |  30 |   20 | 240
```

```x3/2o5o5o5/4*b

.   . . .      | 120 ♦  12 |   60 |  12  12
---------------+-----+-----+------+--------
x   . . .      |   2 | 720 |   10 |   5   5
---------------+-----+-----+------+--------
x3/2o . .      |   3 |   3 | 2400 |   1   1
---------------+-----+-----+------+--------
x3/2o5o .      ♦  12 |  30 |   20 | 120   *
x3/2o . o5/4*b ♦  12 |  30 |   20 |   * 120
```

```x3/2o5o5/4o5*b

.   . .   .    | 120 ♦  12 |   60 |  12  12
---------------+-----+-----+------+--------
x   . .   .    |   2 | 720 |   10 |   5   5
---------------+-----+-----+------+--------
x3/2o .   .    |   3 |   3 | 2400 |   1   1
---------------+-----+-----+------+--------
x3/2o5o   .    ♦  12 |  30 |   20 | 120   *
x3/2o .   o5*b ♦  12 |  30 |   20 |   * 120
```
```or
.   . .   .       | 120 ♦  12 |   60 |  24
------------------+-----+-----+------+----
x   . .   .       |   2 | 720 |   10 |  10
------------------+-----+-----+------+----
x3/2o .   .       |   3 |   3 | 2400 |   2
------------------+-----+-----+------+----
x3/2o5o   .     & ♦  12 |  30 |   20 | 240
```

```x3/2o5/4o5/4o5/4*b

.   .   .   .      | 120 ♦  12 |   60 |  12  12
-------------------+-----+-----+------+--------
x   .   .   .      |   2 | 720 |   10 |   5   5
-------------------+-----+-----+------+--------
x3/2o   .   .      |   3 |   3 | 2400 |   1   1
-------------------+-----+-----+------+--------
x3/2o5/4o   .      ♦  12 |  30 |   20 | 120   *
x3/2o   .   o5/4*b ♦  12 |  30 |   20 |   * 120
```
```or
.   .   .   .         | 120 ♦  12 |   60 |  24
----------------------+-----+-----+------+----
x   .   .   .         |   2 | 720 |   10 |  10
----------------------+-----+-----+------+----
x3/2o   .   .         |   3 |   3 | 2400 |   2
----------------------+-----+-----+------+----
x3/2o5/4o   .       & ♦  12 |  30 |   20 | 240
```

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