Acronym sricoalsrico, srico || gyro srico
Name small-rhombated-icositetrachoron atop gyrated small-rhombated-icositetrachoron
Circumradius sqrt[15+9 sqrt(2)]/2 = 2.632865
Lace city
in approx. ASCII-art
x3o4x      
           
      o3x4o
           
x3q4o      
           
      o3x4x
           
           
           
w3o4x x3x4x
           
      w3x4o
           
o3w4o      
           
q3x4x x3o4w
           
           
           
o3x4u w3o4q
           
           
           
q3x4x x3o4w
           
o3w4o      
           
      w3x4o
           
w3o4x x3x4x
           
           
           
      o3x4x
           
x3q4o      
           
      o3x4o
           
x3o4x      
           
  |     +-- x3o4x3o (srico)
  +-------- o3x4o3x (gyro srico)
Confer
general polytopal classes:
segmentotera   fundamental lace prisms   scaliform  

Incidence matrix according to Dynkin symbol

xo3ox4xo3ox&#x   → height = sqrt[sqrt(2)-1] = 0.643594
(srico || gyro srico)

o.3o.4o.3o.    | 288   * |   2   4    4   0   0 |  1   4   2   2   4   2   4   2   0   0   0  0 |  2  2  1   2   4   2   2   1   2  0  0  0 | 1  2  1  2  1 0
.o3.o4.o3.o    |   * 288 |   0   0    4   4   2 |  0   0   0   0   2   4   2   4   2   2   4  1 |  0  0  0   2   1   2   2   4   2  1  2  2 | 0  1  2  1  2 1
---------------+---------+----------------------+-----------------------------------------------+-------------------------------------------+----------------
x. .. .. ..    |   2   0 | 288   *    *   *   * |  1   2   0   0   2   0   0   0   0   0   0  0 |  2  1  0   2   2   1   0   0   0  0  0  0 | 1  2  1  1  0 0
.. .. x. ..    |   2   0 |   * 576    *   *   * |  0   1   1   1   0   0   1   0   0   0   0  0 |  1  1  1   0   1   0   1   0   1  0  0  0 | 1  1  0  1  1 0
oo3oo4oo3oo&#x |   1   1 |   *   * 1152   *   * |  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 |   *   *    * 576   * |  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 |   *   *    *   * 288 |  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.3o. .. ..    |   3   0 |   3   0    0   0   0 | 96   *   *   *   *   *   *   *   *   *   *  * |  2  0  0   2   0   0   0   0   0  0  0  0 | 1  2  1  0  0 0
x. .. x. ..    |   4   0 |   2   2    0   0   0 |  * 288   *   *   *   *   *   *   *   *   *  * |  1  1  0   0   1   0   0   0   0  0  0  0 | 1  1  0  1  0 0
.. o.4x. ..    |   4   0 |   0   4    0   0   0 |  *   * 144   *   *   *   *   *   *   *   *  * |  1  0  1   0   0   0   1   0   0  0  0  0 | 1  1  0  0  1 0
.. .. x.3o.    |   3   0 |   0   3    0   0   0 |  *   *   * 192   *   *   *   *   *   *   *  * |  0  1  1   0   0   0   0   0   1  0  0  0 | 1  0  0  1  1 0
xo .. .. ..&#x |   2   1 |   1   0    2   0   0 |  *   *   *   * 576   *   *   *   *   *   *  * |  0  0  0   1   1   1   0   0   0  0  0  0 | 0  1  1  1  0 0
.. ox .. ..&#x |   1   2 |   0   0    2   1   0 |  *   *   *   *   * 576   *   *   *   *   *  * |  0  0  0   1   0   0   1   1   0  0  0  0 | 0  1  1  0  1 0
.. .. xo ..&#x |   2   1 |   0   1    2   0   0 |  *   *   *   *   *   * 576   *   *   *   *  * |  0  0  0   0   1   0   1   0   1  0  0  0 | 0  1  0  1  1 0
.. .. .. ox&#x |   1   2 |   0   0    2   0   1 |  *   *   *   *   *   *   * 576   *   *   *  * |  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   3   0 |  *   *   *   *   *   *   *   * 192   *   *  * |  0  0  0   1   0   0   0   0   0  1  1  0 | 0  1  1  0  0 1
.. .x4.o ..    |   0   4 |   0   0    0   4   0 |  *   *   *   *   *   *   *   *   * 144   *  * |  0  0  0   0   0   0   1   0   0  1  0  1 | 0  1  0  0  1 1
.. .x .. .x    |   0   4 |   0   0    0   2   2 |  *   *   *   *   *   *   *   *   *   * 288  * |  0  0  0   0   0   0   0   1   0  0  1  1 | 0  0  1  0  1 1
.. .. .o3.x    |   0   3 |   0   0    0   0   3 |  *   *   *   *   *   *   *   *   *   *   * 96 |  0  0  0   0   0   0   0   0   2  0  0  2 | 0  0  0  1  2 1
---------------+---------+----------------------+-----------------------------------------------+-------------------------------------------+----------------
x.3o.4x. ..      24   0 |  24  24    0   0   0 |  8  12   6   0   0   0   0   0   0   0   0  0 | 24  *  *   *   *   *   *   *   *  *  *  * | 1  1  0  0  0 0
x. .. x.3o.       6   0 |   3   6    0   0   0 |  0   3   0   2   0   0   0   0   0   0   0  0 |  * 96  *   *   *   *   *   *   *  *  *  * | 1  0  0  1  0 0
.. o.4x.3o.      12   0 |   0  24    0   0   0 |  0   0   6   8   0   0   0   0   0   0   0  0 |  *  * 24   *   *   *   *   *   *  *  *  * | 1  0  0  0  1 0
xo3ox .. ..&#x    3   3 |   3   0    6   3   0 |  1   0   0   0   3   3   0   0   1   0   0  0 |  *  *  * 192   *   *   *   *   *  *  *  * | 0  1  1  0  0 0
xo .. xo ..&#x    4   1 |   2   2    4   0   0 |  0   1   0   0   2   0   2   0   0   0   0  0 |  *  *  *   * 288   *   *   *   *  *  *  * | 0  1  0  1  0 0
xo .. .. ox&#x    2   2 |   1   0    4   0   1 |  0   0   0   0   2   0   0   2   0   0   0  0 |  *  *  *   *   * 288   *   *   *  *  *  * | 0  0  1  1  0 0
.. ox4xo ..&#x    4   4 |   0   4    8   4   0 |  0   0   1   0   0   4   4   0   0   1   0  0 |  *  *  *   *   *   * 144   *   *  *  *  * | 0  1  0  0  1 0
.. ox .. ox&#x    1   4 |   0   0    4   2   2 |  0   0   0   0   0   2   0   2   0   0   1  0 |  *  *  *   *   *   *   * 288   *  *  *  * | 0  0  1  0  1 0
.. .. xo3ox&#x    3   3 |   0   3    6   0   3 |  0   0   0   1   0   0   3   3   0   0   0  1 |  *  *  *   *   *   *   *   * 192  *  *  * | 0  0  0  1  1 0
.o3.x4.o ..       0  12 |   0   0    0  24   0 |  0   0   0   0   0   0   0   0   8   6   0  0 |  *  *  *   *   *   *   *   *   * 24  *  * | 0  1  0  0  0 1
.o3.x .. .x       0   6 |   0   0    0   6   3 |  0   0   0   0   0   0   0   0   2   0   3  0 |  *  *  *   *   *   *   *   *   *  * 96  * | 0  0  1  0  0 1
.. .x4.o3.x       0  24 |   0   0    0  24  24 |  0   0   0   0   0   0   0   0   0   6  12  8 |  *  *  *   *   *   *   *   *   *  *  * 24 | 0  0  0  0  1 1
---------------+---------+----------------------+-----------------------------------------------+-------------------------------------------+----------------
x.3o.4x.3o.     288   0 | 288 576    0   0   0 | 96 288 144 192   0   0   0   0   0   0   0  0 | 24 96 24   0   0   0   0   0   0  0  0  0 | 1  *  *  *  * *
xo3ox4xo ..&#x   24  12 |  24  24   48  24   0 |  8  12   6   0  24  24  24   0   8   6   0  0 |  1  0  0   8  12   0   6   0   0  1  0  0 | * 24  *  *  * *
xo3ox .. ox&#x    3   6 |   3   0   12   6   3 |  1   0   0   0   6   6   0   6   2   0   3  0 |  0  0  0   2   0   3   0   3   0  0  1  0 | *  * 96  *  * *
xo .. xo3ox&#x    6   3 |   3   6   12   0   3 |  0   3   0   2   6   0   6   6   0   0   0  1 |  0  1  0   0   3   3   0   0   2  0  0  0 | *  *  * 96  * *
.. ox4xo3ox&#x   12  24 |   0  24   48  24  24 |  0   0   6   8   0  24  24  24   0   6  12  8 |  0  0  1   0   0   0   6  12   8  0  0  1 | *  *  *  * 24 *
.o3.x4.o3.x       0 288 |   0   0    0 576 288 |  0   0   0   0   0   0   0   0 192 144 288 96 |  0  0  0   0   0   0   0   0   0 24 96 24 | *  *  *  *  * 1
or
o.3o.4o.3o.    & | 576 |   2    4    4 |   1   4   2   2    6    6 |  2   2  1   4   5   2   2 | 1  3   3
-----------------+-----+---------------+---------------------------+---------------------------+---------
x. .. .. ..    & |   2 | 576    *    * |   1   2   0   0    2    0 |  2   1  0   2   2   1   0 | 1  2   2
.. .. x. ..    & |   2 |   * 1152    * |   0   1   1   1    0    1 |  1   1  1   1   1   0   1 | 1  2   1
oo3oo4oo3oo&#x   |   2 |   *    * 1152 |   0   0   0   0    2    2 |  0   0  0   2   2   1   1 | 0  2   2
-----------------+-----+---------------+---------------------------+---------------------------+---------
x.3o. .. ..    & |   3 |   3    0    0 | 192   *   *   *    *    * |  2   0  0   2   0   0   0 | 1  2   1
x. .. x. ..    & |   4 |   2    2    0 |   * 576   *   *    *    * |  1   1  0   0   1   0   0 | 1  1   1
.. o.4x. ..    & |   4 |   0    4    0 |   *   * 288   *    *    * |  1   0  1   0   0   0   1 | 1  2   0
.. .. x.3o.    & |   3 |   0    3    0 |   *   *   * 384    *    * |  0   1  1   1   0   0   0 | 1  1   1
xo .. .. ..&#x & |   3 |   1    0    2 |   *   *   *   * 1152    * |  0   0  0   1   1   1   0 | 0  1   2
.. ox .. ..&#x & |   3 |   0    1    2 |   *   *   *   *    * 1152 |  0   0  0   1   1   0   1 | 0  2   1
-----------------+-----+---------------+---------------------------+---------------------------+---------
x.3o.4x. ..    &   24 |  24   24    0 |   8  12   6   0    0    0 | 48   *  *   *   *   *   * | 1  1   0
x. .. x.3o.    &    6 |   3    6    0 |   0   3   0   2    0    0 |  * 192  *   *   *   *   * | 1  0   1
.. o.4x.3o.    &   12 |   0   24    0 |   0   0   6   8    0    0 |  *   * 48   *   *   *   * | 1  1   0
xo3ox .. ..&#x &    6 |   3    3    6 |   1   0   0   1    3    3 |  *   *  * 384   *   *   * | 0  1   1
xo .. xo ..&#x &    5 |   2    2    4 |   0   1   0   0    2    2 |  *   *  *   * 576   *   * | 0  1   1
xo .. .. ox&#x      4 |   2    0    4 |   0   0   0   0    4    0 |  *   *  *   *   * 288   * | 0  0   2
.. ox4xo ..&#x      8 |   0    8    8 |   0   0   2   0    0    8 |  *   *  *   *   *   * 144 | 0  2   0
-----------------+-----+---------------+---------------------------+---------------------------+---------
x.3o.4x.3o.    &  288 | 288  576    0 |  96 288 144 192    0    0 | 24  96 24   0   0   0   0 | 2  *   *
xo3ox4xo ..&#x &   36 |  24   48   48 |   8  12  12   8   24   48 |  1   0  1   8  12   0   6 | * 48   *
xo3ox .. ox&#x &    9 |   6    6   12 |   1   3   0   2   12    6 |  0   1  0   2   3   3   0 | *  * 192

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