As abstract polytope grawvixady is isomorphic to swavixady, thereby replacing pentagons by pentagrams, respectively id by gid and giid by siid. – As such grawvixady is a lieutenant.

Incidence matrix according to Dynkin symbol

```o3x3x3o5/4*b

. . . .      | 3600 |    4    2 |    2    4    2    1 |   2   1   2
-------------+------+-----------+---------------------+------------
. x . .      |    2 | 7200    * |    1    1    1    0 |   1   1   1
. . x .      |    2 |    * 3600 |    0    2    0    1 |   1   0   2
-------------+------+-----------+---------------------+------------
o3x . .      |    3 |    3    0 | 2400    *    *    * |   1   1   0
. x3x .      |    6 |    3    3 |    * 2400    *    * |   1   0   1
. x . o5/4*b |    5 |    5    0 |    *    * 1440    * |   0   1   1
. . x3o      |    3 |    0    3 |    *    *    * 1200 |   0   0   2
-------------+------+-----------+---------------------+------------
o3x3x .      ♦   12 |   12    6 |    4    4    0    0 | 600   *   *
o3x . o5/4*b ♦   30 |   60    0 |   20    0   12    0 |   * 120   *
. x3x3o5/4*b ♦   60 |   60   60 |    0   20   12   20 |   *   * 120
```

```o3x3x3/2o5*b

. . .   .    | 3600 |    4    2 |    2    4    2    1 |   2   1   2
-------------+------+-----------+---------------------+------------
. x .   .    |    2 | 7200    * |    1    1    1    0 |   1   1   1
. . x   .    |    2 |    * 3600 |    0    2    0    1 |   1   0   2
-------------+------+-----------+---------------------+------------
o3x .   .    |    3 |    3    0 | 2400    *    *    * |   1   1   0
. x3x   .    |    6 |    3    3 |    * 2400    *    * |   1   0   1
. x .   o5*b |    5 |    5    0 |    *    * 1440    * |   0   1   1
. . x3/2o    |    3 |    0    3 |    *    *    * 1200 |   0   0   2
-------------+------+-----------+---------------------+------------
o3x3x   .    ♦   12 |   12    6 |    4    4    0    0 | 600   *   *
o3x .   o5*b ♦   30 |   60    0 |   20    0   12    0 |   * 120   *
. x3x3/2o5*b ♦   60 |   60   60 |    0   20   12   20 |   *   * 120
```

```o3/2x3x3o5/4*b

.   . . .      | 3600 |    4    2 |    2    4    2    1 |   2   1   2
---------------+------+-----------+---------------------+------------
.   x . .      |    2 | 7200    * |    1    1    1    0 |   1   1   1
.   . x .      |    2 |    * 3600 |    0    2    0    1 |   1   0   2
---------------+------+-----------+---------------------+------------
o3/2x . .      |    3 |    3    0 | 2400    *    *    * |   1   1   0
.   x3x .      |    6 |    3    3 |    * 2400    *    * |   1   0   1
.   x . o5/4*b |    5 |    5    0 |    *    * 1440    * |   0   1   1
.   . x3o      |    3 |    0    3 |    *    *    * 1200 |   0   0   2
---------------+------+-----------+---------------------+------------
o3/2x3x .      ♦   12 |   12    6 |    4    4    0    0 | 600   *   *
o3/2x . o5/4*b ♦   30 |   60    0 |   20    0   12    0 |   * 120   *
.   x3x3o5/4*b ♦   60 |   60   60 |    0   20   12   20 |   *   * 120
```

```o3/2x3x3/2o5*b

.   . .   .    | 3600 |    4    2 |    2    4    2    1 |   2   1   2
---------------+------+-----------+---------------------+------------
.   x .   .    |    2 | 7200    * |    1    1    1    0 |   1   1   1
.   . x   .    |    2 |    * 3600 |    0    2    0    1 |   1   0   2
---------------+------+-----------+---------------------+------------
o3/2x .   .    |    3 |    3    0 | 2400    *    *    * |   1   1   0
.   x3x   .    |    6 |    3    3 |    * 2400    *    * |   1   0   1
.   x .   o5*b |    5 |    5    0 |    *    * 1440    * |   0   1   1
.   . x3/2o    |    3 |    0    3 |    *    *    * 1200 |   0   0   2
---------------+------+-----------+---------------------+------------
o3/2x3x   .    ♦   12 |   12    6 |    4    4    0    0 | 600   *   *
o3/2x .   o5*b ♦   30 |   60    0 |   20    0   12    0 |   * 120   *
.   x3x3/2o5*b ♦   60 |   60   60 |    0   20   12   20 |   *   * 120
```