As abstract polytope giphiddix is isomorphic to sphiddix, thereby replacing pentagons by pentagrams, resp. pip by stip and giid by siid. – As such giphiddix is a lieutenant.

Incidence matrix according to Dynkin symbol

```x3x3x5o3/2*b

. . . .      | 7200 |    1    2    2 |    2    2    2    1    1 |   2   1   1   1
-------------+------+----------------+--------------------------+----------------
x . . .      |    2 | 3600    *    * |    2    2    0    0    0 |   2   1   1   0
. x . .      |    2 |    * 7200    * |    1    0    1    1    0 |   1   1   0   1
. . x .      |    2 |    *    * 7200 |    0    1    1    0    1 |   1   0   1   1
-------------+------+----------------+--------------------------+----------------
x3x . .      |    6 |    3    3    0 | 2400    *    *    *    * |   1   1   0   0
x . x .      |    4 |    2    0    2 |    * 3600    *    *    * |   1   0   1   0
. x3x .      |    6 |    0    3    3 |    *    * 2400    *    * |   1   0   0   1
. x . o3/2*b |    3 |    0    3    0 |    *    *    * 2400    * |   0   1   0   1
. . x5o      |    5 |    0    0    5 |    *    *    *    * 1440 |   0   0   1   1
-------------+------+----------------+--------------------------+----------------
x3x3x .      ♦   24 |   12   12   12 |    4    6    4    0    0 | 600   *   *   *
x3x . o3/2*b ♦   12 |    6   12    0 |    4    0    0    4    0 |   * 600   *   *
x . x5o      ♦   10 |    5    0   10 |    0    5    0    0    2 |   *   * 720   *
. x3x5o3/2*b ♦   60 |    0   60   60 |    0    0   20   20   12 |   *   *   * 120
```

```x3x3x5/4o3*b

. . .   .    | 7200 |    1    2    2 |    2    2    2    1    1 |   2   1   1   1
-------------+------+----------------+--------------------------+----------------
x . .   .    |    2 | 3600    *    * |    2    2    0    0    0 |   2   1   1   0
. x .   .    |    2 |    * 7200    * |    1    0    1    1    0 |   1   1   0   1
. . x   .    |    2 |    *    * 7200 |    0    1    1    0    1 |   1   0   1   1
-------------+------+----------------+--------------------------+----------------
x3x .   .    |    6 |    3    3    0 | 2400    *    *    *    * |   1   1   0   0
x . x   .    |    4 |    2    0    2 |    * 3600    *    *    * |   1   0   1   0
. x3x   .    |    6 |    0    3    3 |    *    * 2400    *    * |   1   0   0   1
. x .   o3*b |    3 |    0    3    0 |    *    *    * 2400    * |   0   1   0   1
. . x5/4o    |    5 |    0    0    5 |    *    *    *    * 1440 |   0   0   1   1
-------------+------+----------------+--------------------------+----------------
x3x3x   .    ♦   24 |   12   12   12 |    4    6    4    0    0 | 600   *   *   *
x3x .   o3*b ♦   12 |    6   12    0 |    4    0    0    4    0 |   * 600   *   *
x . x5/4o    ♦   10 |    5    0   10 |    0    5    0    0    2 |   *   * 720   *
. x3x5/4o3*b ♦   60 |    0   60   60 |    0    0   20   20   12 |   *   *   * 120
```