Acronym ricoalrico, rico || gyro rico
Name rectified icositetrachoron atop gyrated rectified icositetrachoron
Circumradius sqrt[7+4 sqrt(2)]/2 = 1.778824
Lace city
in approx. ASCII-art
  o3x4o   x3x4o   x3o4q   x3x4o   o3x4o  		-- o3x4o3o (rico)
                                         
                                         
                                         
                                         
o3o4x o3q4o q3o4x o3o4u q3o4x o3q4o o3o4x		-- o3o4x3o (gyro rico)
Confer
general polytopal classes:
segmentotera   fundamental lace prisms   scaliform  

Incidence matrix according to Dynkin symbol

oo3xo4ox3oo&#x   → height = sqrt[4 sqrt(2)-5] = 0.810465
(rico || gyro rico)

o.3o.4o.3o.    | 96  * |   6   3   0 |  3   6   6   3   0  0 |  3  2  3   6  1  0  0 | 1  3  2 0
.o3.o4.o3.o    |  * 96 |   0   3   6 |  0   0   3   6   6  3 |  0  0  1   6  3  2  3 | 0  2  3 1
---------------+-------+-------------+-----------------------+-----------------------+----------
.. x. .. ..    |  2  0 | 288   *   * |  1   2   1   0   0  0 |  2  1  1   2  0  0  0 | 1  2  1 0
oo3oo4oo3oo&#x |  1  1 |   * 288   * |  0   0   2   2   0  0 |  0  0  1   4  1  0  0 | 0  2  2 0
.. .. ..x..    |  0  2 |   *   * 288 |  0   0   0   1   2  1 |  0  0  0   2  1  1  2 | 0  1  2 1
---------------+-------+-------------+-----------------------+-----------------------+----------
o.3x. .. ..    |  3  0 |   3   0   0 | 96   *   *   *   *  * |  2  0  1   0  0  0  0 | 1  2  0 0
.. x.4o. ..    |  4  0 |   4   0   0 |  * 144   *   *   *  * |  1  1  0   1  0  0  0 | 1  1  1 0
.. xo .. ..&#x |  2  1 |   1   2   0 |  *   * 288   *   *  * |  0  0  1   2  0  0  0 | 0  2  1 0
.. .. ox ..&#x |  1  2 |   0   2   1 |  *   *   * 288   *  * |  0  0  0   2  1  0  0 | 0  1  2 0
.. .o4.x ..    |  0  4 |   0   0   4 |  *   *   *   * 144  * |  0  0  0   1  0  1  1 | 0  1  1 1
.. .. .x3.o    |  0  3 |   0   0   3 |  *   *   *   *   * 96 |  0  0  0   0  1  0  2 | 0  0  2 1
---------------+-------+-------------+-----------------------+-----------------------+----------
o.3x.4o. ..     12  0 |  24   0   0 |  8   6   0   0   0  0 | 24  *  *   *  *  *  * | 1  1  0 0
.. x.4o.3o.      8  0 |  12   0   0 |  0   6   0   0   0  0 |  * 24  *   *  *  *  * | 1  0  1 0
oo3xo .. ..&#x   3  1 |   3   3   0 |  1   0   3   0   0  0 |  *  * 96   *  *  *  * | 0  2  0 0
.. xo4ox ..&#x   4  4 |   4   8   4 |  0   1   4   4   1  0 |  *  *  * 144  *  *  * | 0  1  1 0
.. .. ox3oo&#x   1  3 |   0   3   3 |  0   0   0   3   0  1 |  *  *  *   * 96  *  * | 0  0  2 0
.o3.o4.x ..      0  8 |   0   0  12 |  0   0   0   0   6  0 |  *  *  *   *  * 24  * | 0  1  0 1
.. .o4.x3.o      0 12 |   0   0  24 |  0   0   0   0   6  8 |  *  *  *   *  *  * 24 | 0  0  1 1
---------------+-------+-------------+-----------------------+-----------------------+----------
o.3x.4o.3o.     96  0 | 288   0   0 | 96 144   0   0   0  0 | 24 24  0   0  0  0  0 | 1  *  * *
oo3xo4ox ..&#x  12  8 |  24  24  12 |  8   6  24  12   6  0 |  1  0  8   6  0  1  0 | * 24  * *
.. xo4ox3oo&#x   8 12 |  12  24  24 |  0   6  12  24   6  8 |  0  1  0   6  8  0  1 | *  * 24 *
.o3.o4.x3.o      0 96 |   0   0 288 |  0   0   0   0 144 96 |  0  0  0   0  0 24 24 | *  *  * 1
or
o.3o.4o.3o.    & | 192 |   6   3 |   3   6   9 |  3  2   4   6 | 1  5
-----------------+-----+---------+-------------+---------------+-----
.. x. .. ..    & |   2 | 576   * |   1   2   1 |  2  1   1   2 | 1  3
oo3oo4oo3oo&#x   |   2 |   * 288 |   0   0   4 |  0  0   2   4 | 0  4
-----------------+-----+---------+-------------+---------------+-----
o.3x. .. ..    & |   3 |   3   0 | 192   *   * |  2  0   1   0 | 1  2
.. x.4o. ..    & |   4 |   4   0 |   * 288   * |  1  1   0   1 | 1  2
.. xo .. ..&#x & |   3 |   1   2 |   *   * 576 |  0  0   1   2 | 0  3
-----------------+-----+---------+-------------+---------------+-----
o.3x.4o. ..    &   12 |  24   0 |   8   6   0 | 48  *   *   * | 1  1
.. x.4o.3o.    &    8 |  12   0 |   0   6   0 |  * 48   *   * | 1  1
oo3xo .. ..&#x &    4 |   3   3 |   1   0   3 |  *  * 192   * | 0  2
.. xo4ox ..&#x      8 |   8   8 |   0   2   8 |  *  *   * 144 | 0  2
-----------------+-----+---------+-------------+---------------+-----
o.3x.4o.3o.    &   96 | 288   0 |  96 144   0 | 24 24   0   0 | 2  *
oo3xo4ox ..&#x &   20 |  36  24 |   8  12  36 |  1  1   8   6 | * 48

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