Acronym trasteth
Name (triangle,steth)-duoprism
Circumradius sqrt[(11+3 sqrt(2))/6] = 1.593876

As abstract polytope trasteth is isomorphic to tragittith, 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. trasocco by tragocco and stethip by gittithip.


Incidence matrix according to Dynkin symbol

x3o o3o3x4x4/3*d

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

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