As abstract polytope tetsteth is isomorphic to tetgittith, thereby replacing octagons by octagrams, resp. op by stop and socco by gocco, resp. todip by tistodip, soccope by goccope and steth by gittith, resp. otet by stotet, trasocco by tragocco and stethip by gittithip, resp. tetsocco by tetgocco and trasteth by tragittith.

Incidence matrix according to Dynkin symbol

x3o3o o3o3x4x4/3*e

. . . . . . .      | 256 |   3   3   3 |   3   9   9   3   3  3 |  1   9   9   9   9   9  1  1  3 |  3  3   9   9  9  3  3  9 1 |  3  3  3  3  3  9 3 |  1 1 3 3
-------------------+-----+-------------+------------------------+---------------------------------+-----------------------------+---------------------+---------
x . . . . . .      |   2 | 384   *   * |   2   3   3   0   0  0 |  1   6   6   3   3   3  0  0  0 |  3  3   6   6  6  1  1  3 0 |  3  3  3  2  2  6 1 |  1 1 3 2
. . . . . x .      |   2 |   * 384   * |   0   3   0   2   0  1 |  0   3   0   6   0   3  1  0  2 |  1  0   6   0  3  3  0  6 1 |  2  0  1  3  0  6 3 |  1 0 2 3
. . . . . . x      |   2 |   *   * 384 |   0   0   3   0   2  1 |  0   0   3   0   6   3  0  1  2 |  0  1   0   6  3  0  3  6 1 |  0  2  1  0  3  6 3 |  0 1 2 3
-------------------+-----+-------------+------------------------+---------------------------------+-----------------------------+---------------------+---------
x3o . . . . .      |   3 |   3   0   0 | 256   *   *   *   *  * |  1   3   3   0   0   0  0  0  0 |  3  3   3   3  3  0  0  0 0 |  3  3  3  1  1  3 0 |  1 1 3 1
x . . . . x .      |   4 |   2   2   0 |   * 576   *   *   *  * |  0   2   0   2   0   1  0  0  0 |  1  0   4   0  2  1  0  2 0 |  2  0  1  2  0  4 1 |  1 0 2 2
x . . . . . x      |   4 |   2   0   2 |   *   * 576   *   *  * |  0   0   2   0   2   1  0  0  0 |  0  1   0   4  2  0  1  2 0 |  0  2  1  0  2  4 1 |  0 1 2 2
. . . . o3x .      |   3 |   0   3   0 |   *   *   * 256   *  * |  0   0   0   3   0   0  1  0  1 |  0  0   3   0  0  3  0  3 1 |  1  0  0  3  0  3 3 |  1 0 1 3
. . . . o . x4/3*e |   4 |   0   0   4 |   *   *   *   * 192  * |  0   0   0   0   3   0  0  1  1 |  0  0   0   3  0  0  3  3 1 |  0  1  0  0  3  3 3 |  0 1 1 3
. . . . . x4x      |   8 |   0   4   4 |   *   *   *   *   * 96 |  0   0   0   0   0   3  0  0  2 |  0  0   0   0  3  0  0  6 1 |  0  0  1  0  0  6 3 |  0 0 2 3
-------------------+-----+-------------+------------------------+---------------------------------+-----------------------------+---------------------+---------
x3o3o . . . .      ♦   4 |   6   0   0 |   4   0   0   0   0  0 | 64   *   *   *   *   *  *  *  * |  3  3   0   0  0  0  0  0 0 |  3  3  3  0  0  0 0 |  1 1 3 0
x3o . . . x .      ♦   6 |   6   3   0 |   2   3   0   0   0  0 |  * 384   *   *   *   *  *  *  * |  1  0   2   0  1  0  0  0 0 |  2  0  1  1  0  2 0 |  1 0 2 1
x3o . . . . x      ♦   6 |   6   0   3 |   2   0   3   0   0  0 |  *   * 384   *   *   *  *  *  * |  0  1   0   2  1  0  0  0 0 |  0  2  1  0  1  2 0 |  0 1 2 1
x . . . o3x .      ♦   6 |   3   6   0 |   0   3   0   2   0  0 |  *   *   * 384   *   *  *  *  * |  0  0   2   0  0  1  0  1 0 |  1  0  0  2  0  2 1 |  1 0 1 2
x . . . o . x4/3*e ♦   8 |   4   0   8 |   0   0   4   0   2  0 |  *   *   *   * 288   *  *  *  * |  0  0   0   2  0  0  1  1 0 |  0  1  0  0  2  2 1 |  0 1 1 2
x . . . . x4x      ♦  16 |   8   8   8 |   0   4   4   0   0  2 |  *   *   *   *   * 144  *  *  * |  0  0   0   0  2  0  0  2 0 |  0  0  1  0  0  4 1 |  0 0 2 2
. . . o3o3x .      ♦   4 |   0   6   0 |   0   0   0   4   0  0 |  *   *   *   *   *   * 64  *  * |  0  0   0   0  0  3  0  0 1 |  0  0  0  3  0  0 3 |  1 0 0 3
. . . o3o . x4/3*e ♦   8 |   0   0  12 |   0   0   0   0   6  0 |  *   *   *   *   *   *  * 32  * |  0  0   0   0  0  0  3  0 1 |  0  0  0  0  3  0 3 |  0 1 0 3
. . . . o3x4x4/3*e ♦  24 |   0  24  24 |   0   0   0   8   6  6 |  *   *   *   *   *   *  *  * 32 |  0  0   0   0  0  0  0  3 1 |  0  0  0  0  0  3 3 |  0 0 1 3
-------------------+-----+-------------+------------------------+---------------------------------+-----------------------------+---------------------+---------
x3o3o . . x .      ♦   8 |  12   4   0 |   8   6   0   0   0  0 |  2   4   0   0   0   0  0  0  0 | 96  *   *   *  *  *  *  * * |  2  0  1  0  0  0 0 |  1 0 2 0
x3o3o . . . x      ♦   8 |  12   0   4 |   8   0   6   0   0  0 |  2   0   4   0   0   0  0  0  0 |  * 96   *   *  *  *  *  * * |  0  2  1  0  0  0 0 |  0 1 2 0
x3o . . o3x .      ♦   9 |   9   9   0 |   3   9   0   3   0  0 |  0   3   0   3   0   0  0  0  0 |  *  * 256   *  *  *  *  * * |  1  0  0  1  0  1 0 |  1 0 1 1
x3o . . o . x4/3*e ♦  12 |  12   0  12 |   4   0  12   0   3  0 |  0   0   4   0   3   0  0  0  0 |  *  *   * 192  *  *  *  * * |  0  1  0  0  1  1 0 |  0 1 1 1
x3o . . . x4x      ♦  24 |  24  12  12 |   8  12  12   0   0  3 |  0   4   4   0   0   3  0  0  0 |  *  *   *   * 96  *  *  * * |  0  0  1  0  0  2 0 |  0 0 2 1
x . . o3o3x .      ♦   8 |   4  12   0 |   0   6   0   8   0  0 |  0   0   0   4   0   0  2  0  0 |  *  *   *   *  * 96  *  * * |  0  0  0  2  0  0 1 |  1 0 0 2
x . . o3o . x4/3*e ♦  16 |   8   0  24 |   0   0  12   0  12  0 |  0   0   0   0   6   0  0  2  0 |  *  *   *   *  *  * 48  * * |  0  0  0  0  2  0 1 |  0 1 0 2
x . . . o3x4x4/3*e ♦  48 |  24  48  48 |   0  24  24  16  12 12 |  0   0   0   8   6   6  0  0  2 |  *  *   *   *  *  *  * 48 * |  0  0  0  0  0  2 1 |  0 0 1 2
. . . o3o3x4x4/3*e ♦  64 |   0  96  96 |   0   0   0  64  48 24 |  0   0   0   0   0   0 16  8  8 |  *  *   *   *  *  *  *  * 4 |  0  0  0  0  0  0 3 |  0 0 0 3
-------------------+-----+-------------+------------------------+---------------------------------+-----------------------------+---------------------+---------
x3o3o . o3x .      ♦  12 |  18  12   0 |  12  18   0   4   0  0 |  3  12   0   6   0   0  0  0  0 |  3  0   4   0  0  0  0  0 0 | 64  *  *  *  *  * * |  1 0 1 0
x3o3o . o . x4/3*e ♦  16 |  24   0  16 |  16   0  24   0   4  0 |  4   0  16   0   6   0  0  0  0 |  0  4   0   4  0  0  0  0 0 |  * 48  *  *  *  * * |  0 1 1 0
x3o3o . . x4x      ♦  32 |  48  16  16 |  32  24  24   0   0  4 |  8  16  16   0   0   6  0  0  0 |  4  4   0   0  4  0  0  0 0 |  *  * 24  *  *  * * |  0 0 2 0
x3o . o3o3x .      ♦  12 |  12  18   0 |   4  18   0  12   0  0 |  0   6   0  12   0   0  3  0  0 |  0  0   4   0  0  3  0  0 0 |  *  *  * 64  *  * * |  1 0 0 1
x3o . o3o . x4/3*e ♦  24 |  24   0  36 |   8   0  36   0  18  0 |  0   0  12   0  18   0  0  3  0 |  0  0   0   6  0  0  3  0 0 |  *  *  *  * 32  * * |  0 1 0 1
x3o . . o3x4x4/3*e ♦  72 |  72  72  72 |  24  72  72  24  18 18 |  0  24  24  24  18  18  0  0  3 |  0  0   8   6  6  0  0  3 0 |  *  *  *  *  * 32 * |  0 0 1 1
x . . o3o3x4x4/3*e ♦ 128 |  64 192 192 |   0  96  96 128  96 48 |  0   0   0  64  48  24 32 16 16 |  0  0   0   0  0 16  8  8 2 |  *  *  *  *  *  * 6 |  0 0 0 2
-------------------+-----+-------------+------------------------+---------------------------------+-----------------------------+---------------------+---------
x3o3o o3o3x .      ♦  16 |  24  24   0 |  16  36   0  16   0  0 |  4  24   0  24   0   0  4  0  0 |  6  0  16   0  0  6  0  0 0 |  4  0  0  4  0  0 0 | 16 * * *
x3o3o o3o . x4/3*e ♦  32 |  48   0  48 |  32   0  72   0  24  0 |  8   0  48   0  36   0  0  4  0 |  0 12   0  24  0  0  6  0 0 |  0  6  0  0  4  0 0 |  * 8 * *
x3o3o . o3x4x4/3*e ♦  96 | 144  96  96 |  96 144 144  32  24 24 | 24  96  96  48  36  36  0  0  4 | 24 24  32  24 24  0  0  6 0 |  8  6  6  0  0  4 0 |  * * 8 *
x3o . o3o3x4x4/3*e ♦ 192 | 192 288 288 |  64 288 288 192 144 72 |  0  96  96 192 144  72 48 24 24 |  0  0  64  48 24 48 24 24 3 |  0  0  0 16  8  8 3 |  * * * 4