As abstract polytope stethip is isomorphic to gittithip, thereby replacing the octagons by octagrams, resp. op by stop and socco by gocco, resp. soccope by goccope and steth by gittith.

Incidence matrix according to Dynkin symbol

x o3o3x4x4*c

. . . . .      | 128 |  1   3   3 |  3  3   3  3  3 |  3  3  3  1  1  3 |  1 3 3 1
---------------+-----+------------+-----------------+-------------------+---------
x . . . .      |   2 | 64   *   * |  3  3   0  0  0 |  3  3  3  0  0  0 |  1 1 3 0
. . . x .      |   2 |  * 192   * |  1  0   2  0  1 |  2  0  1  1  0  2 |  1 0 2 1
. . . . x      |   2 |  *   * 192 |  0  1   0  2  1 |  0  2  1  0  1  2 |  0 1 2 1
---------------+-----+------------+-----------------+-------------------+---------
x . . x .      |   4 |  2   2   0 | 96  *   *  *  * |  2  0  1  0  0  0 |  1 0 2 0
x . . . x      |   4 |  2   0   2 |  * 96   *  *  * |  0  2  1  0  0  0 |  0 1 2 0
. . o3x .      |   3 |  0   3   0 |  *  * 128  *  * |  1  0  0  1  0  1 |  1 0 1 1
. . o . x4/3*c |   4 |  0   0   4 |  *  *   * 96  * |  0  1  0  0  1  1 |  0 1 1 1
. . . x4x      |   8 |  0   4   4 |  *  *   *  * 48 |  0  0  1  0  0  2 |  0 0 2 1
---------------+-----+------------+-----------------+-------------------+---------
x . o3x .      ♦   6 |  3   6   0 |  3  0   2  0  0 | 64  *  *  *  *  * |  1 0 1 0
x . o . x4/3*c ♦   8 |  4   0   8 |  0  4   0  2  0 |  * 48  *  *  *  * |  0 1 1 0
x . . x4x      ♦  16 |  8   8   8 |  4  4   0  0  2 |  *  * 24  *  *  * |  0 0 2 0
. o3o3x .      ♦   4 |  0   6   0 |  0  0   4  0  0 |  *  *  * 32  *  * |  1 0 0 1
. o3o . x4/3*c ♦   8 |  0   0  12 |  0  0   0  6  0 |  *  *  *  * 16  * |  0 1 0 1
. . o3x4x4/3*c ♦  24 |  0  24  24 |  0  0   8  6  6 |  *  *  *  *  * 16 |  0 0 1 1
---------------+-----+------------+-----------------+-------------------+---------
x o3o3x .      ♦   8 |  4  12   0 |  6  0   8  0  0 |  4  0  0  2  0  0 | 16 * * *
x o3o . x4/3*c ♦  16 |  8   0  24 |  0 12   0 12  0 |  0  6  0  0  2  0 |  * 8 * *
x . o3x4x4/3*c ♦  48 | 24  48  48 | 24 24  16 12 12 |  8  6  6  0  0  2 |  * * 8 *
. o3o3x4x4/3*c ♦  64 |  0  96  96 |  0  0  64 48 24 |  0  0  0 16  8  8 |  * * * 2