As abstract polytope sid thipady is isomorphic to gid thipady, thereby replacing pentagrams by pentagons and interchanging decagrams and decagons, respectively replacing quit gissid by tid, stip by pip, and sidditdid by gidditdid.

Likewise it is isomorphic to mipthi, thereby interchanging decagrams and decagons only, respectively replacing quit gissid by tid, sidditdid by gaddid.

Further it is isomorphic to gapthi, thereby replacing pentagons by pentagrams, respectively stip by pip and sidditdid by saddid.

As such sid thipady is a lieutenant.

Incidence matrix according to Dynkin symbol

```x5/3x3o5/3x5*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
---------------+------+----------------+--------------------------+----------------
x5/3x .   .    |   10 |    5    5    0 | 1440    *    *    *    * |   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
.   . o5/3x    |    5 |    0    0    5 |    *    *    *    * 1440 |   0   0   1   1
---------------+------+----------------+--------------------------+----------------
x5/3x3o   .    ♦   60 |   30   60    0 |   12    0   20    0    0 | 120   *   *   *
x5/3x .   x5*b ♦  120 |   60   60   60 |   12   30    0   12    0 |   * 120   *   *
x   . o5/3x    ♦   10 |    5    0   10 |    0    5    0    0    2 |   *   * 720   *
.   x3o5/3x5*b ♦   60 |    0   60   60 |    0    0   20   12   12 |   *   *   * 120
```

```x5/3x3/2o5/2x5*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
-----------------+------+----------------+--------------------------+----------------
x5/3x   .   .    |   10 |    5    5    0 | 1440    *    *    *    * |   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
.   .   o5/2x    |    5 |    0    0    5 |    *    *    *    * 1440 |   0   0   1   1
-----------------+------+----------------+--------------------------+----------------
x5/3x3/2o   .    ♦   60 |   30   60    0 |   12    0   20    0    0 | 120   *   *   *
x5/3x   .   x5*b ♦  120 |   60   60   60 |   12   30    0   12    0 |   * 120   *   *
x   .   o5/2x    ♦   10 |    5    0   10 |    0    5    0    0    2 |   *   * 720   *
.   x3/2o5/2x5*b ♦   60 |    0   60   60 |    0    0   20   12   12 |   *   *   * 120
```