As abstract polytope spixady is isomorphic to gippixady, thereby replacing pentagons by pentagrams and decagons by decagrams, respectively grid by gaquatid, pip by stip, and saddid by gaddid. – As such spixady is a lieutenant.

Incidence matrix according to Dynkin symbol

```x3x3o5/4x5*b

. . .   .    | 7200 |    1    2    2 |    2    2    1    2    1 |   1   2   1   1
-------------+------+----------------+--------------------------+----------------
x . .   .    |    2 | 3600    *    * |    2    2    0    0    0 |   1   2   1   0
. x .   .    |    2 |    * 7200    * |    1    0    1    1    0 |   1   1   0   1
. . .   x    |    2 |    *    * 7200 |    0    1    0    1    1 |   0   1   1   1
-------------+------+----------------+--------------------------+----------------
x3x .   .    |    6 |    3    3    0 | 2400    *    *    *    * |   1   1   0   0
x . .   x    |    4 |    2    0    2 |    * 3600    *    *    * |   0   1   1   0
. x3o   .    |    3 |    0    3    0 |    *    * 2400    *    * |   1   0   0   1
. x .   x5*b |   10 |    0    5    5 |    *    *    * 1440    * |   0   1   0   1
. . o5/4x    |    5 |    0    0    5 |    *    *    *    * 1440 |   0   0   1   1
-------------+------+----------------+--------------------------+----------------
x3x3o   .    ♦   12 |    6   12    0 |    4    0    4    0    0 | 600   *   *   *
x3x .   x5*b ♦  120 |   60   60   60 |   20   30    0   12    0 |   * 120   *   *
x . o5/4x    ♦   10 |    5    0   10 |    0    5    0    0    2 |   *   * 720   *
. x3o5/4x5*b ♦   60 |    0   60   60 |    0    0   20   12   12 |   *   *   * 120
```

```x3x3/2o5x5*b

. .   . .    | 7200 |    1    2    2 |    2    2    1    2    1 |   1   2   1   1
-------------+------+----------------+--------------------------+----------------
x .   . .    |    2 | 3600    *    * |    2    2    0    0    0 |   1   2   1   0
. x   . .    |    2 |    * 7200    * |    1    0    1    1    0 |   1   1   0   1
. .   . x    |    2 |    *    * 7200 |    0    1    0    1    1 |   0   1   1   1
-------------+------+----------------+--------------------------+----------------
x3x   . .    |    6 |    3    3    0 | 2400    *    *    *    * |   1   1   0   0
x .   . x    |    4 |    2    0    2 |    * 3600    *    *    * |   0   1   1   0
. x3/2o .    |    3 |    0    3    0 |    *    * 2400    *    * |   1   0   0   1
. x   . x5*b |   10 |    0    5    5 |    *    *    * 1440    * |   0   1   0   1
. .   o5x    |    5 |    0    0    5 |    *    *    *    * 1440 |   0   0   1   1
-------------+------+----------------+--------------------------+----------------
x3x3/2o .    ♦   12 |    6   12    0 |    4    0    4    0    0 | 600   *   *   *
x3x   . x5*b ♦  120 |   60   60   60 |   20   30    0   12    0 |   * 120   *   *
x .   o5x    ♦   10 |    5    0   10 |    0    5    0    0    2 |   *   * 720   *
. x3/2o5x5*b ♦   60 |    0   60   60 |    0    0   20   12   12 |   *   *   * 120
```