Acronym ritarico
Name rectified-tesseract atop rectified-icositetrachoron,
rectified-tesseract-first segment of small-prismated-triacontiditeron
Circumradius sqrt(7/2) = 1.870829
Lace city
in approx. ASCII-art
       o3x4o  o3o4q  o3x4o       	-- o3o3x4o (rit)
                                 
                                 
                                 
o3x4o  x3x4o  x3o4q  x3x4o  o3x4o	-- x3o3x4o (rico)
Lace hyper city
in approx. ASCII-art
                           
                           
                           
      x4o   o4q   x4o      
                           
                           
      o4q         o4q      
                           
                           
      x4o   o4q   x4o      
                           
                           
                           
      x4o   o4q   x4o      
                           
                           
x4o   u4o   x4q   u4o   x4o
                           
                           
o4q   x4q         x4q   o4q
                           
                           
x4o   u4o   x4q   u4o   x4o
                           
                           
      x4o   o4q   x4o      
Confer
uniform relative:
spat  
related segmentotera:
copatoe  
general polytopal classes:
segmentotera   lace simplices  

Incidence matrix according to Dynkin symbol

ox3oo3xx4oo&#x   → height = 1/sqrt(2) = 0.707107
(rit || rico)

o.3o.3o.4o.    | 32  * |  6  3  0   0 |  6  3  3  12  0  0  0  0 |  2 3  1  6  6  6  0  0 0 | 1  2  3 3 0
.o3.o3.o4.o    |  * 96 |  0  1  2   4 |  0  0  2   4  1  4  2  2 |  0 0  1  4  2  2  2  2 1 | 0  2  2 1 1
---------------+-------+--------------+--------------------------+--------------------------+------------
.. .. x. ..    |  2  0 | 96  *  *   * |  2  1  0   2  0  0  0  0 |  1 2  0  1  2  2  0  0 0 | 1  1  1 2 0
oo3oo3oo4oo&#x |  1  1 |  * 96  *   * |  0  0  2   4  0  0  0  0 |  0 0  1  4  2  2  0  0 0 | 0  2  2 1 0
.x .. .. ..    |  0  2 |  *  * 96   * |  0  0  1   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   1  0  1  1  1 |  0 0  0  1  1  1  1  1 1 | 0  1  1 1 1
---------------+-------+--------------+--------------------------+--------------------------+------------
.. o.3x. ..    |  3  0 |  3  0  0   0 | 64  *  *   *  *  *  *  * |  1 1  0  0  1  0  0  0 0 | 1  1  0 1 0
.. .. x.4o.    |  4  0 |  4  0  0   0 |  * 24  *   *  *  *  *  * |  0 2  0  0  0  2  0  0 0 | 1  0  1 2 0
ox .. .. ..&#x |  1  2 |  0  2  1   0 |  *  * 96   *  *  *  *  * |  0 0  1  2  0  0  0  0 0 | 0  2  1 0 0
.. .. xx ..&#x |  2  2 |  1  2  0   1 |  *  *  * 192  *  *  *  * |  0 0  0  1  1  1  0  0 0 | 0  1  1 1 0
.x3.o .. ..    |  0  3 |  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  2   2 |  *  *  *   *  * 96  *  * |  0 0  0  1  0  0  1  1 0 | 0  1  1 0 1
.. .o3.x ..    |  0  3 |  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   4 |  *  *  *   *  *  *  * 48 |  0 0  0  0  0  1  0  1 1 | 0  0  1 1 1
---------------+-------+--------------+--------------------------+--------------------------+------------
o.3o.3x. ..      4  0 |  6  0  0   0 |  4  0  0   0  0  0  0  0 | 16 *  *  *  *  *  *  * * | 1  1  0 0 0
.. o.3x.4o.     12  0 | 24  0  0   0 |  8  6  0   0  0  0  0  0 |  * 8  *  *  *  *  *  * * | 1  0  0 1 0
ox3oo .. ..&#x   1  3 |  0  3  3   0 |  0  0  3   0  1  0  0  0 |  * * 32  *  *  *  *  * * | 0  2  0 0 0
ox .. xx ..&#x   2  4 |  1  4  2   2 |  0  0  2   2  0  1  0  0 |  * *  * 96  *  *  *  * * | 0  1  1 0 0
.. oo3xx ..&#x   3  3 |  3  3  0   3 |  1  0  0   3  0  0  1  0 |  * *  *  * 64  *  *  * * | 0  1  0 1 0
.. .. xx4oo&#x   4  4 |  4  4  0   4 |  0  1  0   4  0  0  0  1 |  * *  *  *  * 48  *  * * | 0  0  1 1 0
.x3.o3.x ..      0 12 |  0  0 12  12 |  0  0  0   0  4  6  4  0 |  * *  *  *  *  * 16  * * | 0  1  0 0 1
.x .. .x4.o      0  8 |  0  0  4   8 |  0  0  0   0  0  4  0  2 |  * *  *  *  *  *  * 24 * | 0  0  1 0 1
.. .o3.x4.o      0 12 |  0  0  0  24 |  0  0  0   0  0  0  8  6 |  * *  *  *  *  *  *  * 8 | 0  0  0 1 1
---------------+-------+--------------+--------------------------+--------------------------+------------
o.3o.3x.4o.     32  0 | 96  0  0   0 | 64 24  0   0  0  0  0  0 | 16 8  0  0  0  0  0  0 0 | 1  *  * * *
ox3oo3xx ..&#x   4 12 |  6 12 12  12 |  4  0 12  12  4  6  4  0 |  1 0  4  6  4  0  1  0 0 | * 16  * * *
ox .. xx4oo&#x   4  8 |  4  8  4   8 |  0  1  4   8  0  4  0  2 |  0 0  0  4  0  2  0  1 0 | *  * 24 * *
.. oo3xx4oo&#x  12 12 | 24 12  0  24 |  8  6  0  24  0  0  8  6 |  0 1  0  0  8  6  0  0 1 | *  *  * 8 *
.x3.o3.x4.o      0 96 |  0  0 96 192 |  0  0  0   0 32 96 64 48 |  0 0  0  0  0  0 16 24 8 | *  *  * * 1

ox3oo3xx *b3xx&#x   → height = 1/sqrt(2) = 0.707107
(rit || rico)

o.3o.3o. *b3o.    | 32  * |  3  3  3  0  0  0 |  3  3  3  3  6  6  0  0  0  0  0  0 | 1 1 3  1  3  3  3  3  6 0 0  0 0 | 1 1 1  3 3 0
.o3.o3.o *b3.o    |  * 96 |  0  0  1  2  2  2 |  0  0  0  2  2  2  1  2  2  1  1  2 | 0 0 0  1  2  2  1  1  2 1 1  2 1 | 0 1 1  2 1 1
------------------+-------+-------------------+-------------------------------------+----------------------------------+-------------
.. .. x.    ..    |  2  0 | 48  *  *  *  *  * |  2  0  1  0  2  0  0  0  0  0  0  0 | 1 0 2  0  1  0  2  0  2 0 0  0 0 | 1 1 0  1 2 0
.. .. ..    .x    |  2  0 |  * 48  *  *  *  * |  0  2  1  0  0  2  0  0  0  0  0  0 | 0 1 2  0  0  1  0  2  2 0 0  0 0 | 1 0 1  1 2 0
oo3oo3oo *b3oo&#x |  1  1 |  *  * 96  *  *  * |  0  0  0  2  2  2  0  0  0  0  0  0 | 0 0 0  1  2  2  1  1  2 0 0  0 0 | 0 1 1  2 1 0
.x .. ..    ..    |  0  2 |  *  *  * 96  *  * |  0  0  0  1  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  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  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 0 1  0  0  0  1  0  0 0 0  0 0 | 1 1 0  0 1 0
.. o. .. *b3x.    |  3  0 |  0  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
.. .. x.    x.    |  4  0 |  2  2  0  0  0  0 |  *  * 24  *  *  *  *  *  *  *  *  * | 0 0 2  0  0  0  0  0  2 0 0  0 0 | 1 0 0  1 2 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
.. .. xx    ..&#x |  2  2 |  1  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.3o.3x.    ..      4  0 |  6  0  0  0  0  0 |  4  0  0  0  0  0  0  0  0  0  0  0 | 8 * *  *  *  *  *  *  * * *  * * | 1 1 0  0 0 0
o.3o. .. *b3x.      4  0 |  0  6  0  0  0  0 |  0  4  0  0  0  0  0  0  0  0  0  0 | * 8 *  *  *  *  *  *  * * *  * * | 1 0 1  0 0 0
.. o.3x. *b3x.     12  0 | 12 12  0  0  0  0 |  4  4  6  0  0  0  0  0  0  0  0  0 | * * 8  *  *  *  *  *  * * *  * * | 1 0 0  0 1 0
ox3oo ..    ..&#x   1  3 |  0  0  3  3  0  0 |  0  0  0  3  0  0  1  0  0  0  0  0 | * * * 32  *  *  *  *  * * *  * * | 0 1 1  0 0 0
ox .. xx    ..&#x   2  4 |  1  0  4  2  2  0 |  0  0  0  2  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  2  0  0  1  0  0  0 | * * *  *  * 48  *  *  * * *  * * | 0 0 1  1 0 0
.. oo3xx    ..&#x   3  3 |  3  0  3  0  3  0 |  1  0  0  0  3  0  0  0  0  1  0  0 | * * *  *  *  * 32  *  * * *  * * | 0 1 0  0 1 0
.. oo .. *b3xx&#x   3  3 |  0  3  3  0  0  3 |  0  1  0  0  0  3  0  0  0  0  1  0 | * * *  *  *  *  * 32  * * *  * * | 0 0 1  0 1 0
.. .. xx    xx&#x   4  4 |  2  2  4  0  2  2 |  0  0  1  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  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  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  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  4  4  6 | * * *  *  *  *  *  *  * * *  * 8 | 0 0 0  0 1 1
------------------+-------+-------------------+-------------------------------------+----------------------------------+-------------
o.3o.3x. *b3x.     32  0 | 48 48  0  0  0  0 | 32 32 24  0  0  0  0  0  0  0  0  0 | 8 8 8  0  0  0  0  0  0 0 0  0 0 | 1 * *  * * *
ox3oo3xx    ..&#x   4 12 |  6  0 12 12 12  0 |  4  0  0 12 12  0  4  6  0  4  0  0 | 1 0 0  4  6  0  4  0  0 1 0  0 0 | * 8 *  * * *
ox3oo .. *b3xx&#x   4 12 |  0  6 12 12  0 12 |  0  4  0 12  0 12  4  0  6  0  4  0 | 0 1 0  4  0  6  0  4  0 0 1  0 0 | * * 8  * * *
ox .. xx    xx&#x   4  8 |  2  2  8  4  4  4 |  0  0  1  4  4  4  0  2  2  0  0  2 | 0 0 0  0  2  2  0  0  2 0 0  1 0 | * * * 24 * *
.. oo3xx *b3xx&#x  12 12 | 12 12 12  0 12 12 |  4  4  6  0 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 32 48 48 32 32 48 | 0 0 0  0  0  0  0  0  0 8 8 24 8 | * * *  * * 1

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