As abstract polytope gektabcadont is isomorphic to skatbacadint, thereby replacing octagons by octagrams, resp. socco by gocco and op by stop, resp. steth by gittith, soccope by goccope, and todip by tistodip. – As such gektabcadont is a lieutenant.

Incidence matrix according to Dynkin symbol

```x3o3o3x4x4/3*c

. . . . .      | 640 |   3   3   3 |   3   6   6   3   3   3 |   1   3   3   3   3   6   1  1  3 |  1  1  3  3  1
---------------+-----+-------------+-------------------------+-----------------------------------+---------------
x . . . .      |   2 | 960   *   * |   2   2   2   0   0   0 |   1   2   2   1   1   2   0  0  0 |  1  1  2  1  0
. . . x .      |   2 |   * 960   * |   0   2   0   2   0   1 |   0   1   0   2   0   2   1  0  2 |  1  0  1  2  1
. . . . x      |   2 |   *   * 960 |   0   0   2   0   2   1 |   0   0   1   0   2   2   0  1  2 |  0  1  1  2  1
---------------+-----+-------------+-------------------------+-----------------------------------+---------------
x3o . . .      |   3 |   3   0   0 | 640   *   *   *   *   * |   1   1   1   0   0   0   0  0  0 |  1  1  1  0  0
x . . x .      |   4 |   2   2   0 |   * 960   *   *   *   * |   0   1   0   1   0   1   0  0  0 |  1  0  1  1  0
x . . . x      |   4 |   2   0   2 |   *   * 960   *   *   * |   0   0   1   0   1   1   0  0  0 |  0  1  1  1  0
. . o3x .      |   3 |   0   3   0 |   *   *   * 640   *   * |   0   0   0   1   0   0   1  0  1 |  1  0  0  1  1
. . o . x4/3*c |   4 |   0   0   4 |   *   *   *   * 480   * |   0   0   0   0   1   0   0  1  1 |  0  1  0  1  1
. . . x4x      |   8 |   0   4   4 |   *   *   *   *   * 240 |   0   0   0   0   0   2   0  0  2 |  0  0  1  2  1
---------------+-----+-------------+-------------------------+-----------------------------------+---------------
x3o3o . .      ♦   4 |   6   0   0 |   4   0   0   0   0   0 | 160   *   *   *   *   *   *  *  * |  1  1  0  0  0
x3o . x .      ♦   6 |   6   3   0 |   2   3   0   0   0   0 |   * 320   *   *   *   *   *  *  * |  1  0  1  0  0
x3o . . x      ♦   6 |   6   0   3 |   2   0   3   0   0   0 |   *   * 320   *   *   *   *  *  * |  0  1  1  0  0
x . o3x .      ♦   6 |   3   6   0 |   0   3   0   2   0   0 |   *   *   * 320   *   *   *  *  * |  1  0  0  1  0
x . o . x4/3*c ♦   8 |   4   0   8 |   0   0   4   0   2   0 |   *   *   *   * 240   *   *  *  * |  0  1  0  1  0
x . . x4x      ♦  16 |   8   8   8 |   0   4   4   0   0   2 |   *   *   *   *   * 240   *  *  * |  0  0  1  1  0
. o3o3x .      ♦   4 |   0   6   0 |   0   0   0   4   0   0 |   *   *   *   *   *   * 160  *  * |  1  0  0  0  1
. o3o . x4/3*c ♦   8 |   0   0  12 |   0   0   0   0   6   0 |   *   *   *   *   *   *   * 80  * |  0  1  0  0  1
. . o3x4x4/3*c ♦  24 |   0  24  24 |   0   0   0   8   6   6 |   *   *   *   *   *   *   *  * 80 |  0  0  0  1  1
---------------+-----+-------------+-------------------------+-----------------------------------+---------------
x3o3o3x .      ♦  20 |  30  30   0 |  20  30   0  20   0   0 |   5  10   0  10   0   0   5  0  0 | 32  *  *  *  *
x3o3o . x4/3*c ♦  64 |  96   0  96 |  64   0  96   0  48   0 |  16   0  32   0  24   0   0  8  0 |  * 10  *  *  *
x3o . x4x      ♦  24 |  24  12  12 |   8  12  12   0   0   3 |   0   4   4   0   0   3   0  0  0 |  *  * 80  *  *
x . o3x4x4/3*c ♦  48 |  24  48  48 |   0  24  24  16  12  12 |   0   0   0   8   6   6   0  0  2 |  *  *  * 40  *
. o3o3x4x4/3*c ♦  64 |   0  96  96 |   0   0   0  64  48  24 |   0   0   0   0   0   0  16  8  8 |  *  *  *  * 10
```