Acronym tetocta
Name tetrahedron-octahedron-duoprismatic alterprism,
tet-first medial segment of broc
Circumradius sqrt(15)/4 = 0.968246
Face vector 48, 312, 688, 728, 412, 124, 18
Confer
uniform relative:
broc  
general polytopal classes:
scaliform   segmentoexa   lace simplices  

Incidence matrix according to Dynkin symbol

oo3ox3xo oo3xo3ox&#x   → height = 1/2
(tetoct || alt. tetoct)

o.3o.3o. o.3o.3o.    & | 48 |  3  4   6 |  3  12  2  2  18   9 |  1 12  6  6 1  8 12  12  15  3 |  4  6  6  3  5 10  7 18  9 | 2 2 3  7  4  2  8  6 | 1 3 5
-----------------------+----+-----------+----------------------+--------------------------------+----------------------------+----------------------+------
.. .. x. .. .. ..    & |  2 | 72  *   * |  2   4  0  0   0   2 |  1  8  2  2 0  0  4   0   4  1 |  4  4  4  1  2  0  2  8  4 | 2 2 2  4  2  0  4  4 | 1 2 4
.. .. .. .. x. ..    & |  2 |  * 96   * |  0   3  1  1   3   0 |  0  3  3  3 1  3  3   3   3  0 |  1  3  3  3  3  4  3  6  3 | 1 1 3  4  3  1  4  3 | 1 2 4
oo3oo3oo oo3oo3oo&#x   |  2 |  *  * 144 |  0   0  0  0   4   2 |  0  0  0  0 0  2  4   4   4  1 |  0  0  0  0  2  4  2  8  4 | 0 0 0  4  2  1  4  4 | 0 2 4
-----------------------+----+-----------+----------------------+--------------------------------+----------------------------+----------------------+------
.. o.3x. .. .. ..    & |  3 |  3  0   0 | 48   *  *  *   *   * |  1  4  0  0 0  0  2   0   0  0 |  4  2  2  0  2  0  0  4  1 | 2 2 1  4  1  0  2  2 | 1 2 3
.. .. x. .. x. ..    & |  4 |  2  2   0 |  * 144  *  *   *   * |  0  2  1  1 0  0  0   0   1  0 |  1  2  2  1  0  0  1  2  1 | 1 1 2  1  1  0  2  2 | 1 1 3
.. .. .. o.3x. ..    & |  3 |  0  3   0 |  *   * 32  *   *   * |  0  0  3  0 1  3  0   0   0  0 |  0  3  0  3  3  3  3  0  0 | 1 0 3  3  3  1  3  0 | 1 2 3
.. .. .. .. x.3o.    & |  3 |  0  3   0 |  *   *  * 32   *   * |  0  0  0  3 1  0  3   0   0  0 |  0  0  3  3  3  0  0  3  3 | 0 1 3  3  3  0  1  3 | 1 1 4
.. ox .. .. .. ..&#x & |  3 |  0  1   2 |  *   *  *  * 288   * |  0  0  0  0 0  1  1   2   1  0 |  0  0  0  0  1  3  1  4  1 | 0 0 0  3  1  1  3  2 | 0 2 3
.. .. xo .. .. ..&#x & |  3 |  1  0   2 |  *   *  *  *   * 144 |  0  0  0  0 0  0  2   0   2  1 |  0  0  0  0  1  0  1  4  4 | 0 0 0  2  2  0  2  4 | 0 1 4
-----------------------+----+-----------+----------------------+--------------------------------+----------------------------+----------------------+------
o.3o.3x. .. .. ..    &   4 |  6  0   0 |  4   0  0  0   0   0 | 12  *  *  * *  *  *   *   *  * |  4  0  0  0  2  0  0  0  0 | 2 2 0  4  1  0  0  0 | 1 2 2
.. o.3x. .. x. ..    &   6 |  6  3   0 |  2   3  0  0   0   0 |  * 96  *  * *  *  *   *   *  * |  1  1  1  0  0  0  0  1  0 | 1 1 1  1  0  0  1  1 | 1 1 2
.. .. x. o.3x. ..    &   6 |  3  6   0 |  0   3  2  0   0   0 |  *  * 48  * *  *  *   *   *  * |  0  2  0  1  0  0  1  0  0 | 1 0 2  0  1  0  2  0 | 1 1 2
.. .. x. .. x.3o.    &   6 |  3  6   0 |  0   3  0  2   0   0 |  *  *  * 48 *  *  *   *   *  * |  0  0  2  1  0  0  0  0  1 | 0 1 2  0  1  0  0  2 | 1 0 3
.. .. .. o.3x.3o.    &   6 |  0 12   0 |  0   0  4  4   0   0 |  *  *  *  * 8  *  *   *   *  * |  0  0  0  3  3  0  0  0  0 | 0 0 3  3  3  0  0  0 | 1 1 3
oo3ox .. .. .. ..&#x &   4 |  0  3   3 |  0   0  1  0   3   0 |  *  *  *  * * 96  *   *   *  * |  0  0  0  0  1  2  1  0  0 | 0 0 0  2  1  1  2  0 | 0 2 2
.. ox3xo .. .. ..&#x &   6 |  3  3   6 |  1   0  0  1   3   3 |  *  *  *  * *  * 96   *   *  * |  0  0  0  0  1  0  0  2  1 | 0 0 0  2  1  0  2  1 | 0 1 3
.. ox .. .. xo ..&#x     4 |  0  2   4 |  0   0  0  0   4   0 |  *  *  *  * *  *  * 144   *  * |  0  0  0  0  0  2  0  2  0 | 0 0 0  2  0  1  2  1 | 0 2 2
.. ox .. .. .. ox&#x &   5 |  2  2   4 |  0   1  0  0   2   2 |  *  *  *  * *  *  *   * 144  * |  0  0  0  0  0  0  1  2  1 | 0 0 0  1  1  0  2  2 | 0 1 3
.. .. xo .. .. ox&#x     4 |  2  0   4 |  0   0  0  0   0   4 |  *  *  *  * *  *  *   *   * 36 |  0  0  0  0  0  0  0  0  4 | 0 0 0  0  2  0  0  4 | 0 0 4
-----------------------+----+-----------+----------------------+--------------------------------+----------------------------+----------------------+------
o.3o.3x. .. x. ..    &   8 | 12  4   0 |  8   6  0  0   0   0 |  2  4  0  0 0  0  0   0   0  0 | 24  *  *  *  *  *  *  *  * | 1 1 0  1  0  0  0  0 | 1 1 1
.. o.3x. o.3x. ..    &   9 |  9  9   0 |  3   9  3  0   0   0 |  0  3  3  0 0  0  0   0   0  0 |  * 32  *  *  *  *  *  *  * | 1 0 1  0  0  0  1  0 | 1 1 1
.. o.3x. .. x.3o.    &   9 |  9  9   0 |  3   9  0  3   0   0 |  0  3  0  3 0  0  0   0   0  0 |  *  * 32  *  *  *  *  *  * | 0 1 1  0  0  0  0  1 | 1 0 2
.. .. x. o.3x.3o.    &  12 |  6 24   0 |  0  12  8  8   0   0 |  0  0  4  4 2  0  0   0   0  0 |  *  *  * 12  *  *  *  *  * | 0 0 2  0  1  0  0  0 | 1 0 2
oo3ox3xo .. .. ..&#x &  10 |  6 12  12 |  4   0  4  4  12   6 |  1  0  0  0 1  4  4   0   0  0 |  *  *  *  * 24  *  *  *  * | 0 0 0  2  1  0  0  0 | 0 1 2
oo3ox .. .. xo ..&#x &   5 |  0  4   6 |  0   0  1  0   9   0 |  0  0  0  0 0  2  0   3   0  0 |  *  *  *  *  * 96  *  *  * | 0 0 0  1  0  1  1  0 | 0 2 1
oo3ox .. .. .. ox&#x &   7 |  3  6   6 |  0   3  2  0   6   3 |  0  0  1  0 0  2  0   0   3  0 |  *  *  *  *  *  * 48  *  * | 0 0 0  0  1  0  2  0 | 0 1 2
.. ox3xo .. xo ..&#x &   9 |  6  6  12 |  2   3  0  1  12   6 |  0  1  0  0 0  0  2   3   3  0 |  *  *  *  *  *  *  * 96  * | 0 0 0  1  0  0  1  1 | 0 1 2
.. ox3xo .. .. ox&#x &   9 |  6  6  12 |  1   3  0  2   6  12 |  0  0  0  1 0  0  2   0   3  3 |  *  *  *  *  *  *  *  * 48 | 0 0 0  0  1  0  0  2 | 0 0 3
-----------------------+----+-----------+----------------------+--------------------------------+----------------------------+----------------------+------
o.3o.3x. o.3x. ..    &  12 | 18 12   0 | 12  18  4  0   0   0 |  3 12  6  0 0  0  0   0   0  0 |  3  4  0  0  0  0  0  0  0 | 8 * *  *  *  *  *  * | 1 1 0
o.3o.3x. .. x.3o.    &  12 | 18 12   0 | 12  18  0  4   0   0 |  3 12  0  6 0  0  0   0   0  0 |  3  0  4  0  0  0  0  0  0 | * 8 *  *  *  *  *  * | 1 0 1
.. o.3x. o.3x.3o.    &  18 | 18 36   0 |  6  36 12 12   0   0 |  0 12 12 12 3  0  0   0   0  0 |  0  4  4  3  0  0  0  0  0 | * * 8  *  *  *  *  * | 1 0 1
oo3ox3xo .. xo ..&#x &  14 | 12 16  24 |  8   6  4  4  36  12 |  2  4  0  0 1  8  8  12   6  0 |  1  0  0  0  2  4  0  4  0 | * * * 24  *  *  *  * | 0 1 1
oo3ox3xo .. .. ox&#x &  16 | 12 24  24 |  4  12  8  8  24  24 |  1  0  4  4 2  8  8   0  12  6 |  0  0  0  1  2  0  4  0  4 | * * *  * 12  *  *  * | 0 0 2
oo3ox .. oo3xo ..&#x     6 |  0  6   9 |  0   0  2  0  18   0 |  0  0  0  0 0  6  0   9   0  0 |  0  0  0  0  0  6  0  0  0 | * * *  *  * 16  *  * | 0 2 0
oo3ox .. .. xo3ox&#x &  12 |  9 12  18 |  3   9  3  1  27   9 |  0  3  3  0 0  6  3   9   9  0 |  0  1  0  0  0  3  3  3  0 | * * *  *  *  * 32  * | 0 1 1
.. ox3xo .. xo3ox&#x    18 | 18 18  36 |  6  18  0  6  36  36 |  0  6  0  6 0  0  6   9  18  9 |  0  0  2  0  0  0  0  6  6 | * * *  *  *  *  * 16 | 0 0 2
-----------------------+----+-----------+----------------------+--------------------------------+----------------------------+----------------------+------
o.3o.3x. o.3x.3o.    &  24 | 36 48   0 | 24  72 16 16   0   0 |  6 48 24 24 4  0  0   0   0  0 | 12 16 16  6  0  0  0  0  0 | 4 4 4  0  0  0  0  0 | 2 * *
oo3ox3xo oo3xo ..&#x &  18 | 18 24  36 | 12  18  8  4  72  18 |  3 12  6  0 1 24 12  36  18  0 |  3  4  0  0  3 24  6 12  0 | 1 0 0  3  0  4  4  0 | * 8 *
oo3ox3xo .. xo3ox&#x &  30 | 36 48  72 | 18  54 12 16 108  72 |  3 24 12 18 3 24 36  36  54 18 |  3  4  8  3  6 12 12 24 18 | 0 1 1  3  3  0  4  4 | * * 8

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