Acronym thexarico
Name thex atop rico,
ico-first subsegment of sart
Circumradius sqrt(3) = 1.732051
Lace city
in approx. ASCII-art
x3o4o  u3o4o  x3x4o  u3o4o  x3o4o		-- x3x3o4o (thex)
                                 
                                 
                                 
o3x4o  x3x4o  x3o4q  x3x4o  o3x4o		-- x3o3x4o (rico)
o3x3o   o3u3o   x3x3x   o3u3o   o3x3o		-- x3x3o4o (thex)
                                     
                                     
                                     
x3o3x   x3x3x uo3xx3ou  x3x3x   x3o3x		-- x3o3x4o (rico)
Face vector 144, 600, 720, 312, 50
Confer
uniform relative:
sart
general polytopal classes:
segmentotera   lace simplices  

Incidence matrix according to Dynkin symbol

xx3xo3ox4oo&#x   → height = 1/sqrt(2) = 0.707107
(thex || rico)

o.3o.3o.4o.    | 48  * |  1  4   4  0   0 |  4  4  4  4   4  0  0  0  0 |  4 1  4  4  4  1  0  0 0 | 1  4  1 1 0
.o3.o3.o4.o    |  * 96 |  0  0   2  2   4 |  0  0  2  1   4  1  4  2  2 |  0 0  1  4  2  2  2  2 2 | 0  2  2 1 1
---------------+-------+------------------+-----------------------------+--------------------------+------------
x. .. .. ..    |  2  0 | 24  *   *  *   * |  4  0  4  0   0  0  0  0  0 |  4 0  4  4  0  0  0  0 0 | 1  4  1 0 0
.. x. .. ..    |  2  0 |  * 96   *  *   * |  1  2  0  1   0  0  0  0  0 |  2 1  1  0  2  0  0  0 0 | 1  2  0 1 0
oo3oo3oo4oo&#x |  1  1 |  *  * 192  *   * |  0  0  1  1   2  0  0  0  0 |  0 0  1  2  2  1  0  0 0 | 0  2  1 1 0
.x .. .. ..    |  0  2 |  *  *   * 96   * |  0  0  1  0   0  1  2  0  0 |  0 0  1  2  0  0  2  1 0 | 0  2  1 0 1
.. .. .x ..    |  0  2 |  *  *   *  * 192 |  0  0  0  0   1  0  1  1  1 |  0 0  0  1  1  1  1  1 1 | 0  1  1 1 1
---------------+-------+------------------+-----------------------------+--------------------------+------------
x.3x. .. ..    |  6  0 |  3  3   0  0   0 | 32  *  *  *   *  *  *  *  * |  2 0  1  0  0  0  0  0 0 | 1  2  0 0 0
.. x.3o. ..    |  3  0 |  0  3   0  0   0 |  * 64  *  *   *  *  *  *  * |  1 1  0  0  1  0  0  0 0 | 1  1  0 1 0
xx .. .. ..&#x |  2  2 |  1  0   2  1   0 |  *  * 96  *   *  *  *  *  * |  0 0  1  2  0  0  0  0 0 | 0  2  1 0 0
.. xo .. ..&#x |  2  1 |  0  1   2  0   0 |  *  *  * 96   *  *  *  *  * |  0 0  1  0  2  0  0  0 0 | 0  2  0 1 0
.. .. ox ..&#x |  1  2 |  0  0   2  0   1 |  *  *  *  * 192  *  *  *  * |  0 0  0  1  1  1  0  0 0 | 0  1  1 1 0
.x3.o .. ..    |  0  3 |  0  0   0  3   0 |  *  *  *  *   * 32  *  *  * |  0 0  1  0  0  0  2  0 0 | 0  2  0 0 1
.x .. .x ..    |  0  4 |  0  0   0  2   2 |  *  *  *  *   *  * 96  *  * |  0 0  0  1  0  0  1  1 0 | 0  1  1 0 1
.. .o3.x ..    |  0  3 |  0  0   0  0   3 |  *  *  *  *   *  *  * 64  * |  0 0  0  0  1  0  1  0 1 | 0  1  0 1 1
.. .. .x4.o    |  0  4 |  0  0   0  0   4 |  *  *  *  *   *  *  *  * 48 |  0 0  0  0  0  1  0  1 1 | 0  0  1 1 1
---------------+-------+------------------+-----------------------------+--------------------------+------------
x.3x.3o. ..     12  0 |  6 12   0  0   0 |  4  4  0  0   0  0  0  0  0 | 16 *  *  *  *  *  *  * * | 1  1  0 0 0
.. x.3o.4o.      6  0 |  0 12   0  0   0 |  0  8  0  0   0  0  0  0  0 |  * 8  *  *  *  *  *  * * | 1  0  0 1 0
xx3xo .. ..&#x   6  3 |  3  3   6  3   0 |  1  0  3  3   0  1  0  0  0 |  * * 32  *  *  *  *  * * | 0  2  0 0 0
xx .. ox ..&#x   2  4 |  1  0   4  2   2 |  0  0  2  0   2  0  1  0  0 |  * *  * 96  *  *  *  * * | 0  1  1 0 0
.. xo3ox ..&#x   3  3 |  0  3   6  0   3 |  0  1  0  3   3  0  0  1  0 |  * *  *  * 64  *  *  * * | 0  1  0 1 0
.. .. ox4oo&#x   1  4 |  0  0   4  0   4 |  0  0  0  0   4  0  0  0  1 |  * *  *  *  * 48  *  * * | 0  0  1 1 0
.x3.o3.x ..      0 12 |  0  0   0 12  12 |  0  0  0  0   0  4  6  4  0 |  * *  *  *  *  * 16  * * | 0  1  0 0 1
.x .. .x4.o      0  8 |  0  0   0  4   8 |  0  0  0  0   0  0  4  0  2 |  * *  *  *  *  *  * 24 * | 0  0  1 0 1
.. .o3.x4.o      0 12 |  0  0   0  0  24 |  0  0  0  0   0  0  0  8  6 |  * *  *  *  *  *  *  * 8 | 0  0  0 1 1
---------------+-------+------------------+-----------------------------+--------------------------+------------
x.3x.3o.4o.     48  0 | 24 96   0  0   0 | 32 64  0  0   0  0  0  0  0 | 16 8  0  0  0  0  0  0 0 | 1  *  * * *
xx3xo3ox ..&#x  12 12 |  6 12  24 12  12 |  4  4 12 12  12  4  6  4  0 |  1 0  4  6  4  0  1  0 0 | * 16  * * *
xx .. ox4oo&#x   2  8 |  1  0   8  4   8 |  0  0  4  0   8  0  4  0  2 |  0 0  0  4  0  2  0  1 0 | *  * 24 * *
.. xo3ox4oo&#x   6 12 |  0 12  24  0  24 |  0  8  0 12  24  0  0  8  6 |  0 1  0  0  8  6  0  0 1 | *  *  * 8 *
.x3.o3.x4.o      0 96 |  0  0   0 96 192 |  0  0  0  0   0 32 96 64 48 |  0 0  0  0  0  0 16 24 8 | *  *  * * 1

ox3xo3ox *b3xx&#x   → height = 1/sqrt(2) = 0.707107
(thex || rico)

o.3o.3o. *b3o.    | 48  * |  4  1   4  0  0  0 |  2  2  4  2  4  2  4  0  0  0  0  0  0 | 1 2 2  2  1  2  2  4  2 0 0  0 0 | 1 1 2  1 2 0
.o3.o3.o *b3.o    |  * 96 |  0  0   4  2  2  2 |  0  0  0  4  2  4  4  1  2  2  1  1  2 | 0 0 0  2  2  4  2  2  4 1 1  1 1 | 0 1 2  2 2 1
------------------+-------+--------------------+----------------------------------------+----------------------------------+-------------
.. x. ..    ..    |  2  0 | 96  *   *  *  *  * |  1  1  1  0  1  0  0  0  0  0  0  0  0 | 1 1 1  1  0  0  1  1  0 0 0  0 0 | 1 1 1  0 1 0
.. .. ..    x.    |  2  0 |  * 24   *  *  *  * |  0  0  4  0  0  0  4  0  0  0  0  0  0 | 0 2 2  0  0  2  0  4  2 0 0  0 0 | 1 0 2  1 2 0
oo3oo3oo *b3oo&#x |  1  1 |  *  * 192  *  *  * |  0  0  0  1  1  1  1  0  0  0  0  0  0 | 0 0 0  1  1  1  1  1  1 0 0  0 0 | 0 1 1  1 1 0
.x .. ..    ..    |  0  2 |  *  *   * 96  *  * |  0  0  0  1  0  0  0  1  1  1  0  0  0 | 0 0 0  1  1  1  0  0  0 1 1  1 0 | 0 1 1  1 0 1
.. .. .x    ..    |  0  2 |  *  *   *  * 96  * |  0  0  0  0  0  1  0  0  1  0  1  0  1 | 0 0 0  0  1  0  1  0  1 1 0  1 1 | 0 1 0  1 1 1
.. .. ..    .x    |  0  2 |  *  *   *  *  * 96 |  0  0  0  0  0  0  1  0  0  1  0  1  1 | 0 0 0  0  0  1  0  1  1 0 1  1 1 | 0 0 1  1 1 1
------------------+-------+--------------------+----------------------------------------+----------------------------------+-------------
o.3x. ..    ..    |  3  0 |  3  0   0  0  0  0 | 32  *  *  *  *  *  *  *  *  *  *  *  * | 1 1 0  1  0  0  0  0  0 0 0  0 0 | 1 1 1  0 0 0
.. x.3o.    ..    |  3  0 |  3  0   0  0  0  0 |  * 32  *  *  *  *  *  *  *  *  *  *  * | 1 0 1  0  0  0  1  0  0 0 0  0 0 | 1 1 0  0 1 0
.. x. .. *b3x.    |  6  0 |  3  3   0  0  0  0 |  *  * 32  *  *  *  *  *  *  *  *  *  * | 0 1 1  0  0  0  0  1  0 0 0  0 0 | 1 0 1  0 1 0
ox .. ..    ..&#x |  1  2 |  0  0   2  1  0  0 |  *  *  * 96  *  *  *  *  *  *  *  *  * | 0 0 0  1  1  1  0  0  0 0 0  0 0 | 0 1 1  1 0 0
.. xo ..    ..&#x |  2  1 |  1  0   2  0  0  0 |  *  *  *  * 96  *  *  *  *  *  *  *  * | 0 0 0  1  0  0  1  1  0 0 0  0 0 | 0 1 1  0 1 0
.. .. ox    ..&#x |  1  2 |  0  0   2  0  1  0 |  *  *  *  *  * 96  *  *  *  *  *  *  * | 0 0 0  0  1  0  1  0  1 0 0  0 0 | 0 1 0  1 1 0
.. .. ..    xx&#x |  2  2 |  0  1   2  0  0  1 |  *  *  *  *  *  * 96  *  *  *  *  *  * | 0 0 0  0  0  1  0  1  1 0 0  0 0 | 0 0 1  1 1 0
.x3.o ..    ..    |  0  3 |  0  0   0  3  0  0 |  *  *  *  *  *  *  * 32  *  *  *  *  * | 0 0 0  1  0  0  0  0  0 1 1  0 0 | 0 1 1  0 0 1
.x .. .x    ..    |  0  4 |  0  0   0  2  2  0 |  *  *  *  *  *  *  *  * 48  *  *  *  * | 0 0 0  0  1  0  0  0  0 1 0  1 0 | 0 1 0  1 0 1
.x .. ..    .x    |  0  4 |  0  0   0  2  0  2 |  *  *  *  *  *  *  *  *  * 48  *  *  * | 0 0 0  0  0  1  0  0  0 0 1  1 0 | 0 0 1  1 0 1
.. .o3.x    ..    |  0  3 |  0  0   0  0  3  0 |  *  *  *  *  *  *  *  *  *  * 32  *  * | 0 0 0  0  0  0  1  0  0 1 0  0 1 | 0 1 0  0 1 1
.. .o .. *b3.x    |  0  3 |  0  0   0  0  0  3 |  *  *  *  *  *  *  *  *  *  *  * 32  * | 0 0 0  0  0  0  0  1  0 0 1  0 1 | 0 0 1  0 1 1
.. .. .x    .x    |  0  4 |  0  0   0  0  2  2 |  *  *  *  *  *  *  *  *  *  *  *  * 48 | 0 0 0  0  0  0  0  0  1 0 0  1 1 | 0 0 0  1 1 1
------------------+-------+--------------------+----------------------------------------+----------------------------------+-------------
o.3x.3o.    ..      6  0 | 12  0   0  0  0  0 |  4  4  0  0  0  0  0  0  0  0  0  0  0 | 8 * *  *  *  *  *  *  * * *  * * | 1 1 0  0 0 0
o.3x. .. *b3x.     12  0 | 12  6   0  0  0  0 |  4  0  4  0  0  0  0  0  0  0  0  0  0 | * 8 *  *  *  *  *  *  * * *  * * | 1 0 1  0 0 0
.. x.3o. *b3x.     12  0 | 12  6   0  0  0  0 |  0  4  4  0  0  0  0  0  0  0  0  0  0 | * * 8  *  *  *  *  *  * * *  * * | 1 0 0  0 1 0
ox3xo ..    ..&#x   3  3 |  3  0   6  3  0  0 |  1  0  0  3  3  0  0  1  0  0  0  0  0 | * * * 32  *  *  *  *  * * *  * * | 0 1 1  0 0 0
ox .. ox    ..&#x   1  4 |  0  0   4  2  2  0 |  0  0  0  2  0  2  0  0  1  0  0  0  0 | * * *  * 48  *  *  *  * * *  * * | 0 1 0  1 0 0
ox .. ..    xx&#x   2  4 |  0  1   4  2  0  2 |  0  0  0  2  0  0  2  0  0  1  0  0  0 | * * *  *  * 48  *  *  * * *  * * | 0 0 1  1 0 0
.. xo3ox    ..&#x   3  3 |  3  0   6  0  3  0 |  0  1  0  0  3  3  0  0  0  0  1  0  0 | * * *  *  *  * 32  *  * * *  * * | 0 1 0  0 1 0
.. xo .. *b3xx&#x   6  3 |  3  3   6  0  0  3 |  0  0  1  0  3  0  3  0  0  0  0  1  0 | * * *  *  *  *  * 32  * * *  * * | 0 0 1  0 1 0
.. .. ox    xx&#x   2  4 |  0  1   4  0  2  2 |  0  0  0  0  0  2  2  0  0  0  0  0  1 | * * *  *  *  *  *  * 48 * *  * * | 0 0 0  1 1 0
.x3.o3.x    ..      0 12 |  0  0   0 12 12  0 |  0  0  0  0  0  0  0  4  6  0  4  0  0 | * * *  *  *  *  *  *  * 8 *  * * | 0 1 0  0 0 1
.x3.o .. *b3.x      0 12 |  0  0   0 12  0 12 |  0  0  0  0  0  0  0  4  0  6  0  4  0 | * * *  *  *  *  *  *  * * 8  * * | 0 0 1  0 0 1
.x .. .x    .x      0  8 |  0  0   0  4  4  4 |  0  0  0  0  0  0  0  0  2  2  0  0  2 | * * *  *  *  *  *  *  * * * 24 * | 0 0 0  1 0 1
.. .o3.x *b3.x      0 12 |  0  0   0  0 12 12 |  0  0  0  0  0  0  0  0  0  0  4  4  6 | * * *  *  *  *  *  *  * * *  * 8 | 0 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  0  0  0 | 8 8 8  0  0  0  0  0  0 0 0  0 0 | 1 * *  * * *
ox3xo3ox    ..&#x   6 12 | 12  0  24 12 12  0 |  4  4  0 12 12 12  0  4  6  0  4  0  0 | 1 0 0  4  6  0  4  0  0 1 0  0 0 | * 8 *  * * *
ox3xo .. *b3xx&#x  12 12 | 12  6  24 12  0 12 |  4  0  4 12 12  0 12  4  0  6  0  4  0 | 0 1 0  4  0  6  0  4  0 0 1  0 0 | * * 8  * * *
ox .. ox    xx&#x   2  8 |  0  1   8  4  4  4 |  0  0  0  4  0  4  4  0  2  2  0  0  2 | 0 0 0  0  2  2  0  0  2 0 0  1 0 | * * * 24 * *
.. xo3ox *b3xx&#x  12 12 | 12  6  24  0 12 12 |  0  4  4  0 12 12 12  0  0  0  4  4  6 | 0 0 1  0  0  0  4  4  6 0 0  0 1 | * * *  * 8 *
.x3.o3.x *b3.x      0 96 |  0  0   0 96 96 96 |  0  0  0  0  0  0  0 32 48 48 32 32 48 | 0 0 0  0  0  0  0  0  0 8 8 24 8 | * * *  * * 1

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