Acronym taha (old: tahagtah), tah || gyro tah
Name tah alterprism,
tah atop gyro tah
Circumradius sqrt(37/8) = 2.150581
Confer
uniform relative:
pirhin  
general polytopal classes:
scaliform   segmentotera   lace simplices  

Incidence matrix according to Dynkin symbol

xo3xx3ox *b3xx&#x   → height = 1/sqrt(2) = 0.707107
(tah || gyro tah)

o.3o.3o. *b3o.    | 96  * |  1  2  1   2  0  0  0 |  2  1  1  2  2  2  1  2  0  0  0  0 | 1 2 1  2  1  2  1  2  2 0 0 0 | 1 1 2  1 1 0
.o3.o3.o *b3.o    |  * 96 |  0  0  0   2  2  1  1 |  0  0  0  0  1  2  2  2  1  2  2  1 | 0 0 0  1  1  1  2  2  2 1 1 2 | 0 1 1  1 2 1
------------------+-------+-----------------------+-------------------------------------+-------------------------------+-------------
x. .. ..    ..    |  2  0 | 48  *  *   *  *  *  * |  2  1  0  0  2  0  0  0  0  0  0  0 | 1 2 0  2  1  2  0  0  0 0 0 0 | 1 1 2  1 0 0
.. x. ..    ..    |  2  0 |  * 96  *   *  *  *  * |  1  0  1  1  0  1  0  0  0  0  0  0 | 1 1 1  1  0  0  1  1  0 0 0 0 | 1 1 1  0 1 0
.. .. ..    x.    |  2  0 |  *  * 48   *  *  *  * |  0  1  0  2  0  0  0  2  0  0  0  0 | 0 2 1  0  0  2  0  2  1 0 0 0 | 1 0 2  1 1 0
oo3oo3oo *b3oo&#x |  1  1 |  *  *  * 192  *  *  * |  0  0  0  0  1  1  1  1  0  0  0  0 | 0 0 0  1  1  1  1  1  1 0 0 0 | 0 1 1  1 1 0
.. .x ..    ..    |  0  2 |  *  *  *   * 96  *  * |  0  0  0  0  0  1  0  0  1  1  1  0 | 0 0 0  1  0  0  1  1  0 1 1 1 | 0 1 1  0 1 1
.. .. .x    ..    |  0  2 |  *  *  *   *  * 48  * |  0  0  0  0  0  0  2  0  0  2  0  1 | 0 0 0  0  1  0  2  0  2 1 0 2 | 0 1 0  1 2 1
.. .. ..    .x    |  0  2 |  *  *  *   *  *  * 48 |  0  0  0  0  0  0  0  2  0  0  2  1 | 0 0 0  0  0  1  0  2  2 0 1 2 | 0 0 1  1 2 1
------------------+-------+-----------------------+-------------------------------------+-------------------------------+-------------
x.3x. ..    ..    |  6  0 |  3  3  0   0  0  0  0 | 32  *  *  *  *  *  *  *  *  *  *  * | 1 1 0  1  0  0  0  0  0 0 0 0 | 1 1 1  0 0 0
x. .. ..    x.    |  4  0 |  2  0  2   0  0  0  0 |  * 24  *  *  *  *  *  *  *  *  *  * | 0 2 0  0  0  2  0  0  0 0 0 0 | 1 0 2  1 0 0
.. x.3o.    ..    |  3  0 |  0  3  0   0  0  0  0 |  *  * 32  *  *  *  *  *  *  *  *  * | 1 0 1  0  0  0  1  0  0 0 0 0 | 1 1 0  0 1 0
.. x. .. *b3x.    |  6  0 |  0  3  3   0  0  0  0 |  *  *  * 32  *  *  *  *  *  *  *  * | 0 1 1  0  0  0  0  1  0 0 0 0 | 1 0 1  0 1 0
xo .. ..    ..&#x |  2  1 |  1  0  0   2  0  0  0 |  *  *  *  * 96  *  *  *  *  *  *  * | 0 0 0  1  1  1  0  0  0 0 0 0 | 0 1 1  1 0 0
.. xx ..    ..&#x |  2  2 |  0  1  0   2  1  0  0 |  *  *  *  *  * 96  *  *  *  *  *  * | 0 0 0  1  0  0  1  1  0 0 0 0 | 0 1 1  0 1 0
.. .. ox    ..&#x |  1  2 |  0  0  0   2  0  1  0 |  *  *  *  *  *  * 96  *  *  *  *  * | 0 0 0  0  1  0  1  0  1 0 0 0 | 0 1 0  1 1 0
.. .. ..    xx&#x |  2  2 |  0  0  1   2  0  0  1 |  *  *  *  *  *  *  * 96  *  *  *  * | 0 0 0  0  0  1  0  1  1 0 0 0 | 0 0 1  1 1 0
.o3.x ..    ..    |  0  3 |  0  0  0   0  3  0  0 |  *  *  *  *  *  *  *  * 32  *  *  * | 0 0 0  1  0  0  0  0  0 1 1 0 | 0 1 1  0 0 1
.. .x3.x    ..    |  0  6 |  0  0  0   0  3  3  0 |  *  *  *  *  *  *  *  *  * 32  *  * | 0 0 0  0  0  0  1  0  0 1 0 1 | 0 1 0  0 1 1
.. .x .. *b3.x    |  0  6 |  0  0  0   0  3  0  3 |  *  *  *  *  *  *  *  *  *  * 32  * | 0 0 0  0  0  0  0  1  0 0 1 1 | 0 0 1  0 1 1
.. .. .x    .x    |  0  4 |  0  0  0   0  0  2  2 |  *  *  *  *  *  *  *  *  *  *  * 24 | 0 0 0  0  0  0  0  0  2 0 0 2 | 0 0 0  1 2 1
------------------+-------+-----------------------+-------------------------------------+-------------------------------+-------------
x.3x.3o.    ..     12  0 |  6 12  0   0  0  0  0 |  4  0  4  0  0  0  0  0  0  0  0  0 | 8 * *  *  *  *  *  *  * * * * | 1 1 0  0 0 0
x.3x. .. *b3x.     24  0 | 12 12 12   0  0  0  0 |  4  6  0  4  0  0  0  0  0  0  0  0 | * 8 *  *  *  *  *  *  * * * * | 1 0 1  0 0 0
.. x.3o. *b3x.     12  0 |  0 12  6   0  0  0  0 |  0  0  4  4  0  0  0  0  0  0  0  0 | * * 8  *  *  *  *  *  * * * * | 1 0 0  0 1 0
xo3xx ..    ..&#x   6  3 |  3  3  0   6  3  0  0 |  1  0  0  0  3  3  0  0  1  0  0  0 | * * * 32  *  *  *  *  * * * * | 0 1 1  0 0 0
xo .. ox    ..&#x   2  2 |  1  0  0   4  0  1  0 |  0  0  0  0  2  0  2  0  0  0  0  0 | * * *  * 48  *  *  *  * * * * | 0 1 0  1 0 0
xo .. ..    xx&#x   4  2 |  2  0  2   4  0  0  1 |  0  1  0  0  2  0  0  2  0  0  0  0 | * * *  *  * 48  *  *  * * * * | 0 0 1  1 0 0
.. xx3ox    ..&#x   3  6 |  0  3  0   6  3  3  0 |  0  0  1  0  0  3  3  0  0  1  0  0 | * * *  *  *  * 32  *  * * * * | 0 1 0  0 1 0
.. xx .. *b3xx&#x   6  6 |  0  3  3   6  3  0  3 |  0  0  0  1  0  3  0  3  0  0  1  0 | * * *  *  *  *  * 32  * * * * | 0 0 1  0 1 0
.. .. ox    xx&#x   2  4 |  0  0  1   4  0  2  2 |  0  0  0  0  0  0  2  2  0  0  0  1 | * * *  *  *  *  *  * 48 * * * | 0 0 0  1 1 0
.o3.x3.x    ..      0 12 |  0  0  0   0 12  6  0 |  0  0  0  0  0  0  0  0  4  4  0  0 | * * *  *  *  *  *  *  * 8 * * | 0 1 0  0 0 1
.o3.x .. *b3.x      0 12 |  0  0  0   0 12  0  6 |  0  0  0  0  0  0  0  0  4  0  4  0 | * * *  *  *  *  *  *  * * 8 * | 0 0 1  0 0 1
.. .x3.x *b3.x      0 24 |  0  0  0   0 12 12 12 |  0  0  0  0  0  0  0  0  0  4  4  6 | * * *  *  *  *  *  *  * * * 8 | 0 0 0  0 1 1
------------------+-------+-----------------------+-------------------------------------+-------------------------------+-------------
x.3x.3o. *b3x.     96  0 | 48 96 48   0  0  0  0 | 32 24 32 32  0  0  0  0  0  0  0  0 | 8 8 8  0  0  0  0  0  0 0 0 0 | 1 * *  * * *
xo3xx3ox    ..&#x  12 12 |  6 12  0  24 12  6  0 |  4  0  4  0 12 12 12  0  4  4  0  0 | 1 0 0  4  6  0  4  0  0 1 0 0 | * 8 *  * * *
xo3xx .. *b3xx&#x  24 12 | 12 12 12  24 12  0  6 |  4  6  0  4 12 12  0 12  4  0  4  0 | 0 1 0  4  0  6  0  4  0 0 1 0 | * * 8  * * *
xo .. ox    xx&#x   4  4 |  2  0  2   8  0  2  2 |  0  1  0  0  4  0  4  4  0  0  0  1 | 0 0 0  0  2  2  0  0  2 0 0 0 | * * * 24 * *
.. xx3ox *b3xx&#x  12 24 |  0 12  6  24 12 12 12 |  0  0  4  4  0 12 12 12  0  4  4  6 | 0 0 1  0  0  0  4  4  6 0 0 1 | * * *  * 8 *
.o3.x3.x *b3.x      0 96 |  0  0  0   0 96 48 48 |  0  0  0  0  0  0  0  0 32 32 32 24 | 0 0 0  0  0  0  0  0  0 8 8 8 | * * *  * * 1
or
o.3o.3o. *b3o.    & | 192 |  1   2  1   2 |  2  1  1  2   3  2  2 |  1  2  1  3  1  3  2 | 1 1  3  1
--------------------+-----+---------------+-----------------------+----------------------+----------
x. .. ..    ..    & |   2 | 96   *  *   * |  2  1  0  0   2  0  0 |  1  2  0  2  1  2  0 | 1 1  2  1
.. x. ..    ..    & |   2 |  * 192  *   * |  1  0  1  1   0  1  0 |  1  1  1  2  0  0  1 | 1 1  2  0
.. .. ..    x.    & |   2 |  *   * 96   * |  0  1  0  2   0  0  2 |  0  2  1  0  0  3  2 | 1 0  3  1
oo3oo3oo *b3oo&#x   |   2 |  *   *  * 192 |  0  0  0  0   2  1  1 |  0  0  0  2  1  2  1 | 0 1  2  1
--------------------+-----+---------------+-----------------------+----------------------+----------
x.3x. ..    ..    & |   6 |  3   3  0   0 | 64  *  *  *   *  *  * |  1  1  0  1  0  0  0 | 1 1  1  0
x. .. ..    x.    & |   4 |  2   0  2   0 |  * 48  *  *   *  *  * |  0  2  0  0  0  2  0 | 1 0  2  1
.. x.3o.    ..    & |   3 |  0   3  0   0 |  *  * 64  *   *  *  * |  1  0  1  1  0  0  0 | 1 1  1  0
.. x. .. *b3x.    & |   6 |  0   3  3   0 |  *  *  * 64   *  *  * |  0  1  1  0  0  0  1 | 1 0  2  0
xo .. ..    ..&#x & |   3 |  1   0  0   2 |  *  *  *  * 192  *  * |  0  0  0  1  1  1  0 | 0 1  1  1
.. xx ..    ..&#x   |   4 |  0   2  0   2 |  *  *  *  *   * 96  * |  0  0  0  2  0  0  1 | 0 1  2  0
.. .. ..    xx&#x   |   4 |  0   0  2   2 |  *  *  *  *   *  * 96 |  0  0  0  0  0  2  1 | 0 0  2  1
--------------------+-----+---------------+-----------------------+----------------------+----------
x.3x.3o.    ..    &   12 |  6  12  0   0 |  4  0  4  0   0  0  0 | 16  *  *  *  *  *  * | 1 1  0  0
x.3x. .. *b3x.    &   24 | 12  12 12   0 |  4  6  0  4   0  0  0 |  * 16  *  *  *  *  * | 1 0  1  0
.. x.3o. *b3x.    &   12 |  0  12  6   0 |  0  0  4  4   0  0  0 |  *  * 16  *  *  *  * | 1 0  1  0
xo3xx ..    ..&#x &    9 |  3   6  0   6 |  1  0  1  0   3  3  0 |  *  *  * 64  *  *  * | 0 1  1  0
xo .. ox    ..&#x      4 |  2   0  0   4 |  0  0  0  0   4  0  0 |  *  *  *  * 48  *  * | 0 1  0  1
xo .. ..    xx&#x &    6 |  2   0  3   4 |  0  1  0  0   2  0  2 |  *  *  *  *  * 96  * | 0 0  1  1
.. xx .. *b3xx&#x     12 |  0   6  6   6 |  0  0  0  2   0  3  3 |  *  *  *  *  *  * 32 | 0 0  2  0
--------------------+-----+---------------+-----------------------+----------------------+----------
x.3x.3o. *b3x.    &   96 | 48  96 48   0 | 32 24 32 32   0  0  0 |  8  8  8  0  0  0  0 | 2 *  *  *
xo3xx3ox    ..&#x     24 | 12  24  0  24 |  8  0  8  0  24 12  0 |  2  0  0  8  6  0  0 | * 8  *  *
xo3xx .. *b3xx&#x &   36 | 12  24 18  24 |  4  6  4  8  12 12 12 |  0  1  1  4  0  6  4 | * * 16  *
xo .. ox    xx&#x      8 |  4   0  4   8 |  0  2  0  0   8  0  4 |  0  0  0  0  2  4  0 | * *  * 24

s2x3x3o4s

demi( . . . . . ) | 192 |  1   2   2  1 |  2  1  2  2  1   3  2 |  1  2  1  1  3  3  2 |  1 1 1  3
------------------+-----+---------------+-----------------------+----------------------+----------
demi( . x . . . ) |   2 | 96   *   *  * |  2  0  2  0  1   0  0 |  1  2  0  0  3  0  2 |  1 0 1  3
demi( . . x . . ) |   2 |  * 192   *  * |  1  1  0  1  0   0  1 |  1  1  0  1  0  2  1 |  0 1 1  2
      s . 2 . s   |   2 |  *   * 192  * |  0  0  1  1  0   2  0 |  0  1  1  0  2  2  0 |  1 1 0  2
      . . . o4s   |   2 |  *   *   * 96 |  0  0  0  0  1   2  2 |  0  0  1  1  2  2  2 |  1 1 1  2
------------------+-----+---------------+-----------------------+----------------------+----------
demi( . x3x . . ) |   6 |  3   3   0  0 | 64  *  *  *  *   *  * |  1  1  0  0  0  0  1 |  0 0 1  2
demi( . . x3o . ) |   3 |  0   3   0  0 |  * 64  *  *  *   *  * |  1  0  0  1  0  1  0 |  0 1 1  1
      s2x 2 . s   |   4 |  2   0   2  0 |  *  * 96  *  *   *  * |  0  1  0  0  2  0  0 |  1 0 0  2
      s 2 x 2 s   |   4 |  0   2   2  0 |  *  *  * 96  *   *  * |  0  1  0  0  0  2  0 |  0 1 0  2
      . x 2 o4s   |   4 |  2   0   0  2 |  *  *  *  * 48   *  * |  0  0  0  0  2  0  2 |  1 0 1  2
sefa( s . 2 o4s ) |   3 |  0   0   2  1 |  *  *  *  *  * 192  * |  0  0  1  0  1  1  0 |  1 1 0  1
sefa( . . x3o4s ) |   6 |  0   3   0  3 |  *  *  *  *  *   * 64 |  0  0  0  1  0  1  1 |  0 1 1  1
------------------+-----+---------------+-----------------------+----------------------+----------
demi( . x3x3o . )   12 |  6  12   0  0 |  4  4  0  0  0   0  0 | 16  *  *  *  *  *  * |  0 0 1  1
      s2x3x 2 s     12 |  6   6   6  0 |  2  0  3  3  0   0  0 |  * 32  *  *  *  *  * |  0 0 0  2
      s . 2 o4s      4 |  0   0   4  2 |  0  0  0  0  0   4  0 |  *  * 48  *  *  *  * |  1 1 0  0
      . . x3o4s     12 |  0  12   0  6 |  0  4  0  0  0   0  4 |  *  *  * 16  *  *  * |  0 1 1  0
sefa( s2x 2 o4s )    6 |  3   0   4  2 |  0  0  2  0  1   2  0 |  *  *  *  * 96  *  * |  1 0 0  1
sefa( s 2 x3o4s )    9 |  0   6   6  3 |  0  1  0  3  0   3  1 |  *  *  *  *  * 64  * |  0 1 0  1
sefa( . x3x3o4s )   24 | 12  12   0 12 |  4  0  0  0  6   0  4 |  *  *  *  *  *  * 16 |  0 0 1  1
------------------+-----+---------------+-----------------------+----------------------+----------
      s2x 2 o4s      8 |  4   0   8  4 |  0  0  4  0  2   8  0 |  0  0  2  0  4  0  0 | 24 * *  *
      s 2 x3o4s     24 |  0  24  24 12 |  0  8  0 12  0  24  8 |  0  0  6  2  0  8  0 |  * 8 *  *
      . x3x3o4s     96 | 48  96   0 48 | 32 32  0  0 24   0 32 |  8  0  0  8  0  0  8 |  * * 2  *
sefa( s2x3x3o4s )   36 | 18  24  24 12 |  8  4 12 12  6  12  4 |  1  4  0  0  6  4  1 |  * * * 16

starting figure: x x3x3o4x

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