Acronym tethin
Name tetrahedron - hemipenteract duoprism,
vertex figure of trigoh
Circumradius 1
Volume 13/720 = 0.018056
Confer
general polytopal classes:
segmentozetta  

Incidence matrix according to Dynkin symbol

x3o3o x3o3o *e3o3o

. . . . . .    . . | 64 |  3  10 |  3  30  30 |  1  30  90  10  20 | 10  90  30  60  5  5 |  30  30  60 15 15 1 | 10 20 15 15 3 |  5  5 3
-------------------+----+--------+------------+--------------------+----------------------+---------------------+---------------+--------
x . . . . .    . . |  2 | 96   * |  2  10   0 |  1  20  30   0   0 | 10  60  10  20  0  0 |  30  20  40  5  5 0 | 10 20 10 10 1 |  5  5 2
. . . x . .    . . |  2 |  * 320 |  0   3   6 |  0   3  18   3   6 |  1  18   9  18  3  2 |   6   9  18  9  6 1 |  3  6  9  6 3 |  3  2 3
-------------------+----+--------+------------+--------------------+----------------------+---------------------+---------------+--------
x3o . . . .    . . |  3 |  3   0 | 64   *   * |  1  10   0   0   0 | 10  30   0   0  0  0 |  30  10  20  0  0 0 | 10 20  5  5 0 |  5  5 1
x . . x . .    . . |  4 |  2   2 |  * 480   * |  0   2   6   0   0 |  1  12   3   6  0  0 |   6   6  12  3  2 0 |  3  6  6  4 1 |  4  2 2
. . . x3o .    . . |  3 |  0   3 |  *   * 640 |  0   0   3   1   2 |  0   3   3   6  2  1 |   1   3   6  6  3 1 |  1  2  6  3 3 |  2  1 3
-------------------+----+--------+------------+--------------------+----------------------+---------------------+---------------+--------
x3o3o . . .    . .   4 |  6   0 |  4   0   0 | 16   *   *   *   *  10   0   0   0  0  0 |  30   0   0  0  0 0 | 10 20  0  0 0 |  5  5 0
x3o . x . .    . .   6 |  6   3 |  2   3   0 |  * 320   *   *   * |  1   6   0   0  0  0 |   6   3   6  0  0 0 |  3  6  3  2 0 |  3  2 1
x . . x3o .    . .   6 |  3   6 |  0   3   2 |  *   * 960   *   * |  0   2   1   2  0  0 |   1   2   4  2  1 0 |  1  2  4  2 1 |  2  1 2
. . . x3o3o    . .   4 |  0   6 |  0   0   4 |  *   *   * 160   * |  0   0   3   0  2  0 |   0   3   0  6  0 1 |  1  0  6  0 3 |  2  0 3
. . . x3o . *e3o .   4 |  0   6 |  0   0   4 |  *   *   *   * 320 |  0   0   0   3  1  1 |   0   0   3  3  3 1 |  0  1  3  3 3 |  1  1 3
-------------------+----+--------+------------+--------------------+----------------------+---------------------+---------------+--------
x3o3o x . .    . .   8 | 12   4 |  8   6   0 |  2   4   0   0   0 | 80   *   *   *  *  *    6   0   0  0  0 0 |  3  6  0  0 0 |  3  2 0
x3o . x3o .    . .   9 |  9   9 |  3   9   3 |  0   3   3   0   0 |  * 640   *   *  *  * |   1   1   2  0  0 0 |  1  2  2  1 0 |  2  1 1
x . . x3o3o    . .   8 |  4  12 |  0   6   8 |  0   0   4   2   0 |  *   * 240   *  *  * |   0   2   0  2  0 0 |  1  0  4  0 1 |  2  0 2
x . . x3o . *e3o .   8 |  4  12 |  0   6   8 |  0   0   4   0   2 |  *   *   * 480  *  * |   0   0   2  1  1 0 |  0  1  2  2 1 |  1  1 2
. . . x3o3o *e3o .   8 |  0  24 |  0   0  32 |  0   0   0   8   8 |  *   *   *   * 40  * |   0   0   0  3  0 1 |  0  0  3  0 3 |  1  0 3
. . . x3o . *e3o3o   5 |  0  10 |  0   0  10 |  0   0   0   0   5 |  *   *   *   *  * 64 |   0   0   0  0  3 1 |  0  0  0  3 3 |  0  1 3
-------------------+----+--------+------------+--------------------+----------------------+---------------------+---------------+--------
x3o3o x3o .    . .  12 | 18  12 | 12  18   4 |  3  12   6   0   0 |  3   4   0   0  0  0 | 160   *   *  *  * * |  1  2  0  0 0 |  2  1 0
x3o . x3o3o    . .  12 | 12  18 |  4  18  12 |  0   6  12   3   0 |  0   4   3   0  0  0 |   * 160   *  *  * * |  1  0  2  0 0 |  2  0 1
x3o . x3o . *e3o .  12 | 12  18 |  4  18  12 |  0   6  12   0   3 |  0   4   0   3  0  0 |   *   * 320  *  * * |  0  1  1  1 0 |  1  1 1
x . . x3o3o *e3o .  16 |  8  48 |  0  24  64 |  0   0  32  16  16 |  0   0   8   8  2  0 |   *   *   * 60  * * |  0  0  2  0 1 |  1  0 2
x . . x3o . *e3o3o  10 |  5  20 |  0  10  20 |  0   0  10   0  10 |  0   0   0   5  0  2 |   *   *   *  * 96 * |  0  0  0  2 1 |  0  1 2
. . . x3o3o *e3o3o  16 |  0  80 |  0   0 160 |  0   0   0  40  80 |  0   0   0   0 10 16 |   *   *   *  *  * 4 |  0  0  0  0 3 |  0  0 3
-------------------+----+--------+------------+--------------------+----------------------+---------------------+---------------+--------
x3o3o x3o3o    . .  16 | 24  24 | 16  36  16 |  4  24  24   4   0 |  6  16   6   0  0  0 |   4   4   0  0  0 0 | 40  *  *  * * |  2  0 0
x3o3o x3o . *e3o .  16 | 24  24 | 16  36  16 |  4  24  24   0   4 |  6  16   0   6  0  0 |   4   0   4  0  0 0 |  * 80  *  * * |  1  1 0
x3o . x3o3o *e3o .  24 | 24  72 |  8  72  96 |  0  24  96  24  24 |  0  32  24  24  3  0 |   0   8   8  3  0 0 |  *  * 40  * * |  1  0 1
x3o . x3o . *e3o3o  15 | 15  30 |  5  30  30 |  0  10  30   0  15 |  0  10   0  15  0  3 |   0   0   5  0  3 0 |  *  *  * 64 * |  0  1 1
x . . x3o3o *e3o3o  32 | 16 160 |  0  80 320 |  0   0 160  80 160 |  0   0  40  80 20 32 |   0   0   0 10 16 2 |  *  *  *  * 6 |  0  0 2
-------------------+----+--------+------------+--------------------+----------------------+---------------------+---------------+--------
x3o3o x3o3o *e3o .  32 | 48  96 | 32 192 128 |  8  96 192  32  32 | 24 128  48  48  4  0 |  32  32  32  6  0 0 |  8  8  4  0 0 | 10  * *
x3o3o x3o . *e3o3o  20 | 30  40 | 20  60  40 |  5  40  60   0  20 | 10  40   0  30  0  4 |  10   0  20  0  6 0 |  0  5  0  4 0 |  * 16 *
x3o . x3o3o *e3o3o  48 | 48 240 | 16 240 480 |  0  80 480 120 240 |  0 160 120 240 30 48 |   0  40  80 30 48 3 |  0  0 10 16 3 |  *  * 4

ox3oo xx3oo3oo *d3oo3oo&#x   → height = sqrt(2/3) = 0.816497
(hin || trahin)

...

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