Acronym trasinnont
Name (triangle,sinnont)-duoprism
Circumradius sqrt[(25+6 sqrt(2))/12] = 1.670461

As abstract polytope trasinnont is isomorphic to traginnont, 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, stethip by gittithip, and sinnont by ginnont, resp. trasteth by tragittith and sinnontip by ginnontip.


Incidence matrix according to Dynkin symbol

x3o o3o3o3x4x4/3*e

. . . . . . .      | 480 |   2   4   4 |   1   8   8   6   6   4 |   4   4  12  12   8   4   4   6 |   6   6  4   8   8  12  1  1  4 |   4  4  6  2  2  8 1 |  1  1  4 2
-------------------+-----+-------------+-------------------------+---------------------------------+---------------------------------+----------------------+-----------
x . . . . . .      |   2 | 480   *   * |   1   4   4   0   0   0 |   4   4   6   6   4   0   0   0 |   6   6  4   4   4   6  0  0  0 |   4  4  6  1  1  4 0 |  1  1  4 1
. . . . . x .      |   2 |   * 960   * |   0   2   0   3   0   1 |   1   0   6   0   2   3   0   3 |   3   0  1   6   0   6  1  0  3 |   3  0  3  2  0  6 1 |  1  0  3 2
. . . . . . x      |   2 |   *   * 960 |   0   0   2   0   3   1 |   0   1   0   6   2   0   3   3 |   0   3  1   0   6   6  0  1  3 |   0  3  3  0  2  6 1 |  0  1  3 2
-------------------+-----+-------------+-------------------------+---------------------------------+---------------------------------+----------------------+-----------
x3o . . . . .      |   3 |   3   0   0 | 160   *   *   *   *   * |   4   4   0   0   0   0   0   0 |   6   6  4   0   0   0  0  0  0 |   4  4  6  0  0  0 0 |  1  1  4 0
x . . . . x .      |   4 |   2   2   0 |   * 960   *   *   *   * |   1   0   3   0   1   0   0   0 |   3   0  1   3   0   3  0  0  0 |   3  0  3  1  0  3 0 |  1  0  3 1
x . . . . . x      |   4 |   2   0   2 |   *   * 960   *   *   * |   0   1   0   3   1   0   0   0 |   0   3  1   0   3   3  0  0  0 |   0  3  3  0  1  3 0 |  0  1  3 1
. . . . o3x .      |   3 |   0   3   0 |   *   *   * 960   *   * |   0   0   2   0   0   2   0   1 |   1   0  0   4   0   2  1  0  2 |   2  0  1  2  0  4 1 |  1  0  2 2
. . . . o . x4/3*e |   4 |   0   0   4 |   *   *   *   * 720   * |   0   0   0   2   0   0   2   1 |   0   1  0   0   4   2  0  1  2 |   0  2  1  0  2  4 1 |  0  1  2 2
. . . . . x4x      |   8 |   0   4   4 |   *   *   *   *   * 240 |   0   0   0   0   2   0   0   3 |   0   0  1   0   0   6  0  0  3 |   0  0  3  0  0  6 1 |  0  0  3 2
-------------------+-----+-------------+-------------------------+---------------------------------+---------------------------------+----------------------+-----------
x3o . . . x .         6 |   6   3   0 |   2   3   0   0   0   0 | 320   *   *   *   *   *   *   * |   3   0  1   0   0   0  0  0  0 |   3  0  3  0  0  0 0 |  1  0  3 0
x3o . . . . x         6 |   6   0   3 |   2   0   3   0   0   0 |   * 320   *   *   *   *   *   * |   0   3  1   0   0   0  0  0  0 |   0  3  3  0  0  0 0 |  0  1  3 0
x . . . o3x .         6 |   3   6   0 |   0   3   0   2   0   0 |   *   * 960   *   *   *   *   * |   1   0  0   2   0   1  0  0  0 |   2  0  1  1  0  2 0 |  1  0  2 1
x . . . o . x4/3*e    8 |   4   0   8 |   0   0   4   0   2   0 |   *   *   * 720   *   *   *   * |   0   1  0   0   2   1  0  0  0 |   0  2  1  0  1  2 0 |  0  1  2 1
x . . . . x4x        16 |   8   8   8 |   0   4   4   0   0   2 |   *   *   *   * 240   *   *   * |   0   0  1   0   0   3  0  0  0 |   0  0  3  0  0  3 0 |  0  0  3 1
. . . o3o3x .         4 |   0   6   0 |   0   0   0   4   0   0 |   *   *   *   *   * 480   *   * |   0   0  0   2   0   0  1  0  1 |   1  0  0  2  0  2 1 |  1  0  1 2
. . . o3o . x4/3*e    8 |   0   0  12 |   0   0   0   0   6   0 |   *   *   *   *   *   * 240   * |   0   0  0   0   2   0  0  1  1 |   0  1  0  0  2  2 1 |  0  1  1 2
. . . . o3x4x4/3*e   24 |   0  24  24 |   0   0   0   8   6   6 |   *   *   *   *   *   *   * 120 |   0   0  0   0   0   2  0  0  2 |   0  0  1  0  0  4 1 |  0  0  2 2
-------------------+-----+-------------+-------------------------+---------------------------------+---------------------------------+----------------------+-----------
x3o . . o3x .         9 |   9   9   0 |   3   9   0   3   0   0 |   3   0   3   0   0   0   0   0 | 320   *  *   *   *   *  *  *  * |   2  0  1  0  0  0 0 |  1  0  2 0
x3o . . o . x4/3*e   12 |  12   0  12 |   4   0  12   0   3   0 |   0   4   0   3   0   0   0   0 |   * 240  *   *   *   *  *  *  * |   0  2  1  0  0  0 0 |  0  1  2 0
x3o . . . x4x        24 |  24  12  12 |   8  12  12   0   0   3 |   4   4   0   0   3   0   0   0 |   *   * 80   *   *   *  *  *  * |   0  0  3  0  0  0 0 |  0  0  3 0
x . . o3o3x .         8 |   4  12   0 |   0   6   0   8   0   0 |   0   0   4   0   0   2   0   0 |   *   *  * 480   *   *  *  *  * |   1  0  0  1  0  1 0 |  1  0  1 1
x . . o3o . x4/3*e   16 |   8   0  24 |   0   0  12   0  12   0 |   0   0   0   6   0   0   2   0 |   *   *  *   * 240   *  *  *  * |   0  1  0  0  1  1 0 |  0  1  1 1
x . . . o3x4x4/3*e   48 |  24  48  48 |   0  24  24  16  12  12 |   0   0   8   6   6   0   0   2 |   *   *  *   *   * 120  *  *  * |   0  0  1  0  0  2 0 |  0  0  2 1
. . o3o3o3x .         5 |   0  10   0 |   0   0   0  10   0   0 |   0   0   0   0   0   5   0   0 |   *   *  *   *   *   * 96  *  * |   0  0  0  2  0  0 1 |  1  0  0 2
. . o3o3o . x4/3*e   16 |   0   0  32 |   0   0   0   0  24   0 |   0   0   0   0   0   0   8   0 |   *   *  *   *   *   *  * 30  * |   0  0  0  0  2  0 1 |  0  1  0 2
. . . o3o3x4x4/3*e   64 |   0  96  96 |   0   0   0  64  48  24 |   0   0   0   0   0  16   8   8 |   *   *  *   *   *   *  *  * 30 |   0  0  0  0  0  2 1 |  0  0  1 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  0  0 | 160  *  *  *  *  * * |  1  0  1 0
x3o . o3o . x4/3*e   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  0  0 |   * 80  *  *  *  * * |  0  1  1 0
x3o . . o3x4x4/3*e   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  0  0 |   *  * 40  *  *  * * |  0  0  2 0
x . o3o3o3x .        10 |   5  20   0 |   0  10   0  20   0   0 |   0   0  10   0   0  10   0   0 |   0   0  0   5   0   0  2  0  0 |   *  *  * 96  *  * * |  1  0  0 1
x . o3o3o . x4/3*e   32 |  16   0  64 |   0   0  32   0  48   0 |   0   0   0  24   0   0  16   0 |   0   0  0   0   8   0  0  2  0 |   *  *  *  * 30  * * |  0  1  0 1
x . . o3o3x4x4/3*e  128 |  64 192 192 |   0  96  96 128  96  48 |   0   0  64  48  24  32  16  16 |   0   0  0  16   8   8  0  0  2 |   *  *  *  *  * 30 * |  0  0  1 1
. . o3o3o3x4x4/3*e  160 |   0 320 320 |   0   0   0 320 240  80 |   0   0   0   0   0 160  80  40 |   0   0  0   0   0   0 32 10 10 |   *  *  *  *  *  * 3 |  0  0  0 2
-------------------+-----+-------------+-------------------------+---------------------------------+---------------------------------+----------------------+-----------
x3o o3o3o3x .        15 |  15  30   0 |   5  30   0  30   0   0 |  10   0  30   0   0  15   0   0 |  10   0  0  15   0   0  3  0  0 |   5  0  0  3  0  0 0 | 32  *  * *
x3o o3o3o . x4/3*e   48 |  48   0  96 |  16   0  96   0  72   0 |   0  32   0  72   0   0  24   0 |   0  24  0   0  24   0  0  3  0 |   0  8  0  0  3  0 0 |  * 10  * *
x3o . o3o3x4x4/3*e  192 | 192 288 288 |  64 288 288 192 144  72 |  96  96 192 144  72  48  24  24 |  64  48 24  48  24  24  0  0  3 |  16  8  8  0  0  3 0 |  *  * 10 *
x . o3o3o3x4x4/3*e  320 | 160 640 640 |   0 320 320 640 480 160 |   0   0 320 240  80 320 160  80 |   0   0  0 160  80  40 64 20 20 |   0  0  0 32 10 10 2 |  *  *  * 3

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