Acronym teta troct
Name tetrahedron atop triangle-octahedron duoprism
Circumradius sqrt(6/7) = 0.925820
Face vector 22, 96, 160, 130, 56, 12
Confer
uniform relative:
bril  
general polytopal classes:
segmentopeta   lace simplices  

Incidence matrix according to Dynkin symbol

oo3ox oo3ox3xo&#x   → height = sqrt(7/24) = 0.540062
(tet || troct)

o.3o. o.3o.3o.    | 4  * | 3  9  0  0 | 3  9  9  9 0  0  0  0 | 1  3  9  9  3  9  0  0  0 0 |  3 3  3  9 3 0 0 0 | 1 3 3 0
.o3.o .o3.o3.o    | * 18 | 0  2  2  4 | 0  4  4  1 1  8  2  2 | 0  2  8  2  2  2  4  4  4 1 |  4 1  4  4 1 2 2 2 | 2 2 2 1
------------------+------+------------+-----------------------+-----------------------------+--------------------+--------
.. .. .. .. x.    | 2  0 | 6  *  *  * | 2  0  0  3 0  0  0  0 | 1  0  0  3  0  6  0  0  0 0 |  0 1  0  6 3 0 0 0 | 0 2 3 0
oo3oo oo3oo3oo&#x | 1  1 | * 36  *  * | 0  2  2  1 0  0  0  0 | 0  1  4  2  1  2  0  0  0 0 |  2 1  2  4 1 0 0 0 | 1 2 2 0
.. .x .. .. ..    | 0  2 | *  * 18  * | 0  2  0  0 1  4  0  0 | 0  2  4  1  0  0  4  2  2 0 |  4 1  2  2 0 2 2 1 | 2 2 1 1
.. .. .. .x ..    | 0  2 | *  *  * 36 | 0  0  1  0 0  2  1  1 | 0  0  2  0  1  1  1  2  2 1 |  1 0  2  2 1 1 1 2 | 1 1 2 1
------------------+------+------------+-----------------------+-----------------------------+--------------------+--------
.. .. .. o.3x.    | 3  0 | 3  0  0  0 | 4  *  *  * *  *  *  * | 1  0  0  0  0  3  0  0  0 0 |  0 0  0  3 3 0 0 0 | 0 1 3 0
.. ox .. .. ..&#x | 1  2 | 0  2  1  0 | * 36  *  * *  *  *  * | 0  1  2  1  0  0  0  0  0 0 |  2 1  1  2 0 0 0 0 | 1 2 1 0
.. .. .. ox ..&#x | 1  2 | 0  2  0  1 | *  * 36  * *  *  *  * | 0  0  2  0  1  1  0  0  0 0 |  1 0  2  2 1 0 0 0 | 1 1 2 0
.. .. .. .. xo&#x | 2  1 | 1  2  0  0 | *  *  * 18 *  *  *  * | 0  0  0  2  0  2  0  0  0 0 |  0 1  0  4 1 0 0 0 | 0 2 2 0
.o3.x .. .. ..    | 0  3 | 0  0  3  0 | *  *  *  * 6  *  *  * | 0  2  0  0  0  0  4  0  0 0 |  4 1  0  0 0 2 2 0 | 2 2 0 1
.. .x .. .x ..    | 0  4 | 0  0  2  2 | *  *  *  * * 36  *  * | 0  0  1  0  0  0  1  1  1 0 |  1 0  1  1 0 1 1 1 | 1 1 1 1
.. .. .o3.x ..    | 0  3 | 0  0  0  3 | *  *  *  * *  * 12  * | 0  0  0  0  1  0  0  2  0 1 |  0 0  2  0 1 1 0 2 | 1 0 2 1
.. .. .. .x3.o    | 0  3 | 0  0  0  3 | *  *  *  * *  *  * 12 | 0  0  0  0  0  1  0  0  2 1 |  0 0  0  2 1 0 1 2 | 0 1 2 1
------------------+------+------------+-----------------------+-----------------------------+--------------------+--------
.. .. o.3o.3x.     4  0 | 6  0  0  0 | 4  0  0  0 0  0  0  0 | 1  *  *  *  *  *  *  *  * * |  0 0  0  0 3 0 0 0 | 0 0 3 0
oo3ox .. .. ..&#x  1  3 | 0  3  3  0 | 0  3  0  0 1  0  0  0 | * 12  *  *  *  *  *  *  * * |  2 1  0  0 0 0 0 0 | 1 2 0 0
.. ox .. ox ..&#x  1  4 | 0  4  2  2 | 0  2  2  0 0  1  0  0 | *  * 36  *  *  *  *  *  * * |  1 0  1  1 0 0 0 0 | 1 1 1 0
.. ox .. .. xo&#x  2  2 | 1  4  1  0 | 0  2  0  2 0  0  0  0 | *  *  * 18  *  *  *  *  * * |  0 1  0  2 0 0 0 0 | 0 2 1 0
.. .. oo3ox ..&#x  1  3 | 0  3  0  3 | 0  0  3  0 0  0  1  0 | *  *  *  * 12  *  *  *  * * |  0 0  2  0 1 0 0 0 | 1 0 2 0
.. .. .. ox3xo&#x  3  3 | 3  6  0  3 | 1  0  3  3 0  0  0  1 | *  *  *  *  * 12  *  *  * * |  0 0  0  2 1 0 0 0 | 0 1 2 0
.o3.x .. .x ..     0  6 | 0  0  6  3 | 0  0  0  0 2  3  0  0 | *  *  *  *  *  * 12  *  * * |  1 0  0  0 0 1 1 0 | 1 1 0 1
.. .x .o3.x ..     0  6 | 0  0  3  6 | 0  0  0  0 0  3  2  0 | *  *  *  *  *  *  * 12  * * |  0 0  1  0 0 1 0 1 | 1 0 1 1
.. .x .. .x3.o     0  6 | 0  0  3  6 | 0  0  0  0 0  3  0  2 | *  *  *  *  *  *  *  * 12 * |  0 0  0  1 0 0 1 1 | 0 1 1 1
.. .. .o3.x3.o     0  6 | 0  0  0 12 | 0  0  0  0 0  0  4  4 | *  *  *  *  *  *  *  *  * 3 |  0 0  0  0 1 0 0 2 | 0 0 2 1
------------------+------+------------+-----------------------+-----------------------------+--------------------+--------
oo3ox .. ox ..&#x  1  6 | 0  6  6  3 | 0  6  3  0 2  3  0  0 | 0  2  3  0  0  0  1  0  0 0 | 12 *  *  * * * * * | 1 1 0 0
oo3ox .. .. xo&#x  2  3 | 1  6  3  0 | 0  6  0  3 1  0  0  0 | 0  2  0  3  0  0  0  0  0 0 |  * 6  *  * * * * * | 0 2 0 0
.. ox oo3ox ..&#x  1  6 | 0  6  3  6 | 0  3  6  0 0  3  2  0 | 0  0  3  0  2  0  0  1  0 0 |  * * 12  * * * * * | 1 0 1 0
.. ox .. ox3xo&#x  3  6 | 3 12  3  6 | 1  6  6  6 0  3  0  2 | 0  0  3  3  0  2  0  0  1 0 |  * *  * 12 * * * * | 0 1 1 0
.. .. oo3ox3xo&#x  4  6 | 6 12  0 12 | 4  0 12  6 0  0  4  4 | 1  0  0  0  4  4  0  0  0 1 |  * *  *  * 3 * * * | 0 0 2 0
.o3.x .o3.x ..     0  9 | 0  0  9  9 | 0  0  0  0 3  9  3  0 | 0  0  0  0  0  0  3  3  0 0 |  * *  *  * * 4 * * | 1 0 0 1
.o3.x .. .x3.o     0  9 | 0  0  9  9 | 0  0  0  0 3  9  0  3 | 0  0  0  0  0  0  3  0  3 0 |  * *  *  * * * 4 * | 0 1 0 1
.. .x .o3.x3.o     0 12 | 0  0  6 24 | 0  0  0  0 0 12  8  8 | 0  0  0  0  0  0  0  4  4 2 |  * *  *  * * * * 3 | 0 0 1 1
------------------+------+------------+-----------------------+-----------------------------+--------------------+--------
oo3ox oo3ox ..&#x  1  9 | 0  9  9  9 | 0  9  9  0 3  9  3  0 | 0  3  9  0  3  0  3  3  0 0 |  3 0  3  0 0 1 0 0 | 4 * * *
oo3ox .. ox3xo&#x  3  9 | 3 18  9  9 | 1 18  9  9 3  9  0  3 | 0  6  9  9  0  3  3  0  3 0 |  3 3  0  3 0 0 1 0 | * 4 * *
.. ox oo3ox3xo&#x  4 12 | 6 24  6 24 | 4 12 24 12 0 12  8  8 | 1  0 12  6  8  8  0  4  4 2 |  0 0  4  4 2 0 0 1 | * * 3 *
.o3.x .o3.x3.o     0 18 | 0  0 18 36 | 0  0  0  0 6 36 12 12 | 0  0  0  0  0  0 12 12 12 3 |  0 0  0  0 0 4 4 3 | * * * 1

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