As abstract polytope sidipthi is isomorphic to gidipthi, thereby interchanging pentagons and pentagrams, and replacing the decagons by decagrams, respectively gike by ike, gad by sissid, and saddid by gaddid. – As such sidipthi is a lieutenant.

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

Finally it is isomorphic to gisdipthi, thereby maintaining pentagons and pentagrams, but replacing the decagons by decagrams, respectively replacing saddid by gidditdid.

Incidence matrix according to Dynkin symbol

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

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

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

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