Acronym gapthi Name grand prismatotriakishecatonicosachoron Circumradius sqrt[8-sqrt(5)] = 2.400819 Colonel of regiment quippirghi Externallinks

As abstract polytope gapthi is isomorphic to mipthi, thereby replacing pentagons by pentagrams and interchanging decagrams and decagons, respectively replacing quit gissid by tid, pip by stip, and saddid by gaddid.

Likewise it is isomorphic to sid thipady, thereby replacing pentagons by pentagrams, respectively pip by stip and saddid by sidditdid.

Further it is isomorphic to gid thipady, thereby interchanging decagrams and decagons only, respectively replacing quit gissid by tid, saddid by gidditdid.

As such gapthi is a lieutenant.

Incidence matrix according to Dynkin symbol

```x5/3x3o5/4x5*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
---------------+------+----------------+--------------------------+----------------
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
.   . o5/4x    |    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   . o5/4x    ♦   10 |    5    0   10 |    0    5    0    0    2 |   *   * 720   *
.   x3o5/4x5*b ♦   60 |    0   60   60 |    0    0   20   12   12 |   *   *   * 120
```

```x5/3x3/2o5x5*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
---------------+------+----------------+--------------------------+----------------
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
.   .   o5x    |    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   .   o5x    ♦   10 |    5    0   10 |    0    5    0    0    2 |   *   * 720   *
.   x3/2o5x5*b ♦   60 |    0   60   60 |    0    0   20   12   12 |   *   *   * 120
```