Acronym thexagtah
Name thex atop gyrated tah
Circumradius sqrt(45/8) = 2.371708
Confer
general polytopal classes:
segmentotera  

Incidence matrix according to Dynkin symbol

oo3xx3ox *b3xx&#x   → height = 1/sqrt(2) = 0.707107
(thex || gyro tah)

o.3o.3o. *b3o.    | 48  * |  4  1  2  0  0  0 |  1  1  2  4  1  2  0  0  0  0 | 1 2 2  2  2  4  1 0 0 0 | 1 1 2 2 0
.o3.o3.o *b3.o    |  * 96 |  0  0  1  2  1  1 |  0  0  0  2  1  1  1  2  2  1 | 0 0 0  1  2  2  1 1 1 2 | 0 1 1 2 1
------------------+-------+-------------------+-------------------------------+-------------------------+----------
.. x. ..    ..    |  2  0 | 96  *  *  *  *  * |  1  1  1  1  0  0  0  0  0  0 | 1 1 1  1  1  1  0 0 0 0 | 1 1 1 1 0
.. .. ..    x.    |  2  0 |  * 24  *  *  *  * |  0  0  4  0  0  2  0  0  0  0 | 0 2 2  0  0  4  1 0 0 0 | 1 0 2 2 0
oo3oo3oo *b3oo&#x |  1  1 |  *  * 96  *  *  * |  0  0  0  2  1  1  0  0  0  0 | 0 0 0  1  2  2  1 0 0 0 | 0 1 1 2 0
.. .x ..    ..    |  0  2 |  *  *  * 96  *  * |  0  0  0  1  0  0  1  1  1  0 | 0 0 0  1  1  1  0 1 1 1 | 0 1 1 1 1
.. .. .x    ..    |  0  2 |  *  *  *  * 48  * |  0  0  0  0  1  0  0  2  0  1 | 0 0 0  0  2  0  1 1 0 2 | 0 1 0 2 1
.. .. ..    .x    |  0  2 |  *  *  *  *  * 48 |  0  0  0  0  0  1  0  0  2  1 | 0 0 0  0  0  2  1 0 1 2 | 0 0 1 2 1
------------------+-------+-------------------+-------------------------------+-------------------------+----------
o.3x. ..    ..    |  3  0 |  3  0  0  0  0  0 | 32  *  *  *  *  *  *  *  *  * | 1 1 0  1  0  0  0 0 0 0 | 1 1 1 0 0
.. x.3o.    ..    |  3  0 |  3  0  0  0  0  0 |  * 32  *  *  *  *  *  *  *  * | 1 0 1  0  1  0  0 0 0 0 | 1 1 0 1 0
.. x. .. *b3x.    |  6  0 |  3  3  0  0  0  0 |  *  * 32  *  *  *  *  *  *  * | 0 1 1  0  0  1  0 0 0 0 | 1 0 1 1 0
.. xx ..    ..&#x |  2  2 |  1  0  2  1  0  0 |  *  *  * 96  *  *  *  *  *  * | 0 0 0  1  1  1  0 0 0 0 | 0 1 1 1 0
.. .. ox    ..&#x |  1  2 |  0  0  2  0  1  0 |  *  *  *  * 48  *  *  *  *  * | 0 0 0  0  2  0  1 0 0 0 | 0 1 0 2 0
.. .. ..    xx&#x |  2  2 |  0  1  2  0  0  1 |  *  *  *  *  * 48  *  *  *  * | 0 0 0  0  0  2  1 0 0 0 | 0 0 1 2 0
.o3.x ..    ..    |  0  3 |  0  0  0  3  0  0 |  *  *  *  *  *  * 32  *  *  * | 0 0 0  1  0  0  0 1 1 0 | 0 1 1 0 1
.. .x3.x    ..    |  0  6 |  0  0  0  3  3  0 |  *  *  *  *  *  *  * 32  *  * | 0 0 0  0  1  0  0 1 0 1 | 0 1 0 1 1
.. .x .. *b3.x    |  0  6 |  0  0  0  3  0  3 |  *  *  *  *  *  *  *  * 32  * | 0 0 0  0  0  1  0 0 1 1 | 0 0 1 1 1
.. .. .x    .x    |  0  4 |  0  0  0  0  2  2 |  *  *  *  *  *  *  *  *  * 24 | 0 0 0  0  0  0  1 0 0 2 | 0 0 0 2 1
------------------+-------+-------------------+-------------------------------+-------------------------+----------
o.3x.3o.    ..      6  0 | 12  0  0  0  0  0 |  4  4  0  0  0  0  0  0  0  0 | 8 * *  *  *  *  * * * * | 1 1 0 0 0
o.3x. .. *b3x.     12  0 | 12  6  0  0  0  0 |  4  0  4  0  0  0  0  0  0  0 | * 8 *  *  *  *  * * * * | 1 0 1 0 0
.. x.3o. *b3x.     12  0 | 12  6  0  0  0  0 |  0  4  4  0  0  0  0  0  0  0 | * * 8  *  *  *  * * * * | 1 0 0 1 0
oo3xx ..    ..&#x   3  3 |  3  0  3  3  0  0 |  1  0  0  3  0  0  1  0  0  0 | * * * 32  *  *  * * * * | 0 1 1 0 0
.. xx3ox    ..&#x   3  6 |  3  0  6  3  3  0 |  0  1  0  3  3  0  0  1  0  0 | * * *  * 32  *  * * * * | 0 1 0 1 0
.. xx .. *b3xx&#x   6  6 |  3  3  6  3  0  3 |  0  0  1  3  0  3  0  0  1  0 | * * *  *  * 32  * * * * | 0 0 1 1 0
.. .. ox    xx&#x   2  4 |  0  1  4  0  2  2 |  0  0  0  0  2  2  0  0  0  1 | * * *  *  *  * 24 * * * | 0 0 0 2 0
.o3.x3.x    ..      0 12 |  0  0  0 12  6  0 |  0  0  0  0  0  0  4  4  0  0 | * * *  *  *  *  * 8 * * | 0 1 0 0 1
.o3.x .. *b3.x      0 12 |  0  0  0 12  0  6 |  0  0  0  0  0  0  4  0  4  0 | * * *  *  *  *  * * 8 * | 0 0 1 0 1
.. .x3.x *b3.x      0 24 |  0  0  0 12 12 12 |  0  0  0  0  0  0  0  4  4  6 | * * *  *  *  *  * * * 8 | 0 0 0 1 1
------------------+-------+-------------------+-------------------------------+-------------------------+----------
o.3x.3o. *b3x.     48  0 | 96 24  0  0  0  0 | 32 32 32  0  0  0  0  0  0  0 | 8 8 8  0  0  0  0 0 0 0 | 1 * * * *
oo3xx3ox    ..&#x   6 12 | 12  0 12 12  6  0 |  4  4  0 12  6  0  4  4  0  0 | 1 0 0  4  4  0  0 1 0 0 | * 8 * * *
oo3xx .. *b3xx&#x  12 12 | 12  6 12 12  0  6 |  4  0  4 12  0  6  4  0  4  0 | 0 1 0  4  0  4  0 0 1 0 | * * 8 * *
.. xx3ox *b3xx&#x  12 24 | 12  6 24 12 12 12 |  0  4  4 12 12 12  0  4  4  6 | 0 0 1  0  4  4  6 0 0 1 | * * * 8 *
.o3.x3.x *b3.x      0 96 |  0  0  0 96 48 48 |  0  0  0  0  0  0 32 32 32 24 | 0 0 0  0  0  0  0 8 8 8 | * * * * 1

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