As abstract polytope sisdipthi is isomorphic to gisdipthi, thereby interchanging pentagons and pentagrams, and replacing the decagons by decagrams, respectively ike by gike, sissid by gad, and sidditdid by gidditdid.

Further it is isomorphic to sidipthi, thereby likewise interchanging pentagons and pentagrams, but maintaining the decagons, respectively replacing ike by gike, sissid by gad, and sidditdid by saddid.

Finally it is isomorphic to gidipthi, thereby maintaining pentagons and pentagrams, but replacing the decagons by decagrams, respectively replacing sidditdid by gaddid.

Incidence matrix according to Dynkin symbol

```o5o3x5x5/3*b

. . . .      | 1440 |    5    5 |    5    5   5 |   1   1   5
-------------+------+-----------+---------------+------------
. . x .      |    2 | 3600    * |    2    0   1 |   1   0   2
. . . x      |    2 |    * 3600 |    0    2   1 |   0   1   2
-------------+------+-----------+---------------+------------
. o3x .      |    3 |    3    0 | 2400    *   * |   1   0   1
. o . x5/3*b |    5 |    0    5 |    * 1440   * |   0   1   1
. . x5x      |   10 |    5    5 |    *    * 720 |   0   0   2
-------------+------+-----------+---------------+------------
o5o3x .      ♦   12 |   30    0 |   20    0   0 | 120   *   *
o5o . x5/3*b ♦   12 |    0   30 |    0   12   0 |   * 120   *
. o3x5x5/3*b ♦   60 |   60   60 |   20   12  12 |   *   * 120
```

```o5o3/2x5x5/2*b

. .   . .      | 1440 |    5    5 |    5    5   5 |   1   1   5
---------------+------+-----------+---------------+------------
. .   x .      |    2 | 3600    * |    2    0   1 |   1   0   2
. .   . x      |    2 |    * 3600 |    0    2   1 |   0   1   2
---------------+------+-----------+---------------+------------
. o3/2x .      |    3 |    3    0 | 2400    *   * |   1   0   1
. o   . x5/2*b |    5 |    0    5 |    * 1440   * |   0   1   1
. .   x5x      |   10 |    5    5 |    *    * 720 |   0   0   2
---------------+------+-----------+---------------+------------
o5o3/2x .      ♦   12 |   30    0 |   20    0   0 | 120   *   *
o5o   . x5/2*b ♦   12 |    0   30 |    0   12   0 |   * 120   *
. o3/2x5x5/2*b ♦   60 |   60   60 |   20   12  12 |   *   * 120
```

```o5/4o3x5x5/3*b

.   . . .      | 1440 |    5    5 |    5    5   5 |   1   1   5
---------------+------+-----------+---------------+------------
.   . x .      |    2 | 3600    * |    2    0   1 |   1   0   2
.   . . x      |    2 |    * 3600 |    0    2   1 |   0   1   2
---------------+------+-----------+---------------+------------
.   o3x .      |    3 |    3    0 | 2400    *   * |   1   0   1
.   o . x5/3*b |    5 |    0    5 |    * 1440   * |   0   1   1
.   . x5x      |   10 |    5    5 |    *    * 720 |   0   0   2
---------------+------+-----------+---------------+------------
o5/4o3x .      ♦   12 |   30    0 |   20    0   0 | 120   *   *
o5/4o . x5/3*b ♦   12 |    0   30 |    0   12   0 |   * 120   *
.   o3x5x5/3*b ♦   60 |   60   60 |   20   12  12 |   *   * 120
```

```o5/4o3/2x5x5/2*b

.   .   . .      | 1440 |    5    5 |    5    5   5 |   1   1   5
-----------------+------+-----------+---------------+------------
.   .   x .      |    2 | 3600    * |    2    0   1 |   1   0   2
.   .   . x      |    2 |    * 3600 |    0    2   1 |   0   1   2
-----------------+------+-----------+---------------+------------
.   o3/2x .      |    3 |    3    0 | 2400    *   * |   1   0   1
.   o   . x5/2*b |    5 |    0    5 |    * 1440   * |   0   1   1
.   .   x5x      |   10 |    5    5 |    *    * 720 |   0   0   2
-----------------+------+-----------+---------------+------------
o5/4o3/2x .      ♦   12 |   30    0 |   20    0   0 | 120   *   *
o5/4o   . x5/2*b ♦   12 |    0   30 |    0   12   0 |   * 120   *
.   o3/2x5x5/2*b ♦   60 |   60   60 |   20   12  12 |   *   * 120
```