Acronym ... Name sidtixhi+dox (?) Circumradius 1 Coordinates (1, 0, 0, 0)                                         & all permutations, all changes of sign (vertex inscribed q-hex) (1/2, 1/2, 1/2, 1/2)                             & all permutations, all changes of sign (vertex inscribed tes) ((1+sqrt(5))/4, (sqrt(5)-1)/4, 1/4, 0)   & all even permutations, all changes of sign (vertex inscribed v-sadi) General of army ex Colonel of regiment sishi Confer uniform relative: sidtixhi   dox

Looks like a compound of sidtixhi and dox. Its vertex figure is the already degenerate sicdatrid. Accordingly the edges coincide by 3. Also the 2 classes of triangles coincide one by one.

As abstract polytope sidtixhi+dox is isomorphic to gidtixhi+dox, thereby replacing gike by ike.

Incidence matrix according to Dynkin symbol

```x3o5/2o3o3*a

. .   . .    | 120 ♦   60 |   60   60 |  12  30  20
-------------+-----+------+-----------+------------
x .   . .    |   2 | 3600 |    2    2 |   1   2   1
-------------+-----+------+-----------+------------
x3o   . .    |   3 |    3 | 2400    * |   1   1   0
x .   . o3*a |   3 |    3 |    * 2400 |   0   1   1
-------------+-----+------+-----------+------------
x3o5/2o .    ♦  12 |   30 |   20    0 | 120   *   *
x3o   . o3*a ♦   6 |   12 |    4    4 |   * 600   *
x .   o3o3*a ♦   4 |    6 |    0    4 |   *   * 600
```

```x3o5/3o3o3/2*a

. .   . .      | 120 ♦   60 |   60   60 |  12  30  20
---------------+-----+------+-----------+------------
x .   . .      |   2 | 3600 |    2    2 |   1   2   1
---------------+-----+------+-----------+------------
x3o   . .      |   3 |    3 | 2400    * |   1   1   0
x .   . o3/2*a |   3 |    3 |    * 2400 |   0   1   1
---------------+-----+------+-----------+------------
x3o5/3o .      ♦  12 |   30 |   20    0 | 120   *   *
x3o   . o3/2*a ♦   6 |   12 |    4    4 |   * 600   *
x .   o3o3/2*a ♦   4 |    6 |    0    4 |   *   * 600
```

```x3o5/3o3/2o3*a

. .   .   .    | 120 ♦   60 |   60   60 |  12  30  20
---------------+-----+------+-----------+------------
x .   .   .    |   2 | 3600 |    2    2 |   1   2   1
---------------+-----+------+-----------+------------
x3o   .   .    |   3 |    3 | 2400    * |   1   1   0
x .   .   o3*a |   3 |    3 |    * 2400 |   0   1   1
---------------+-----+------+-----------+------------
x3o5/3o   .    ♦  12 |   30 |   20    0 | 120   *   *
x3o   .   o3*a ♦   6 |   12 |    4    4 |   * 600   *
x .   o3/2o3*a ♦   4 |    6 |    0    4 |   *   * 600
```

```x3/2o5/3o3o3*a

.   .   . .    | 120 ♦   60 |   60   60 |  12  30  20
---------------+-----+------+-----------+------------
x   .   . .    |   2 | 3600 |    2    2 |   1   2   1
---------------+-----+------+-----------+------------
x3/2o   . .    |   3 |    3 | 2400    * |   1   1   0
x   .   . o3*a |   3 |    3 |    * 2400 |   0   1   1
---------------+-----+------+-----------+------------
x3/2o5/3o .    ♦  12 |   30 |   20    0 | 120   *   *
x3/2o   . o3*a ♦   6 |   12 |    4    4 |   * 600   *
x   .   o3o3*a ♦   4 |    6 |    0    4 |   *   * 600
```

```x3o5/2o3/2o3/2*a

. .   .   .      | 120 ♦   60 |   60   60 |  12  30  20
-----------------+-----+------+-----------+------------
x .   .   .      |   2 | 3600 |    2    2 |   1   2   1
-----------------+-----+------+-----------+------------
x3o   .   .      |   3 |    3 | 2400    * |   1   1   0
x .   .   o3/2*a |   3 |    3 |    * 2400 |   0   1   1
-----------------+-----+------+-----------+------------
x3o5/2o   .      ♦  12 |   30 |   20    0 | 120   *   *
x3o   .   o3/2*a ♦   6 |   12 |    4    4 |   * 600   *
x .   o3/2o3/2*a ♦   4 |    6 |    0    4 |   *   * 600
```

```x3/2o5/2o3o3/2*a

.   .   . .      | 120 ♦   60 |   60   60 |  12  30  20
-----------------+-----+------+-----------+------------
x   .   . .      |   2 | 3600 |    2    2 |   1   2   1
-----------------+-----+------+-----------+------------
x3/2o   . .      |   3 |    3 | 2400    * |   1   1   0
x   .   . o3/2*a |   3 |    3 |    * 2400 |   0   1   1
-----------------+-----+------+-----------+------------
x3/2o5/2o .      ♦  12 |   30 |   20    0 | 120   *   *
x3/2o   . o3/2*a ♦   6 |   12 |    4    4 |   * 600   *
x   .   o3o3/2*a ♦   4 |    6 |    0    4 |   *   * 600
```

```x3/2o5/2o3/2o3*a

.   .   .   .    | 120 ♦   60 |   60   60 |  12  30  20
-----------------+-----+------+-----------+------------
x   .   .   .    |   2 | 3600 |    2    2 |   1   2   1
-----------------+-----+------+-----------+------------
x3/2o   .   .    |   3 |    3 | 2400    * |   1   1   0
x   .   .   o3*a |   3 |    3 |    * 2400 |   0   1   1
-----------------+-----+------+-----------+------------
x3/2o5/2o   .    ♦  12 |   30 |   20    0 | 120   *   *
x3/2o   .   o3*a ♦   6 |   12 |    4    4 |   * 600   *
x   .   o3/2o3*a ♦   4 |    6 |    0    4 |   *   * 600
```

```x3/2o5/3o3/2o3/2*a

.   .   .   .      | 120 ♦   60 |   60   60 |  12  30  20
-------------------+-----+------+-----------+------------
x   .   .   .      |   2 | 3600 |    2    2 |   1   2   1
-------------------+-----+------+-----------+------------
x3/2o   .   .      |   3 |    3 | 2400    * |   1   1   0
x   .   .   o3/2*a |   3 |    3 |    * 2400 |   0   1   1
-------------------+-----+------+-----------+------------
x3/2o5/3o   .      ♦  12 |   30 |   20    0 | 120   *   *
x3/2o   .   o3/2*a ♦   6 |   12 |    4    4 |   * 600   *
x   .   o3/2o3/2*a ♦   4 |    6 |    0    4 |   *   * 600
```