Acronym	gricoa (old: gricoalgrico)
Name	great-rhombated-icositetrachoron alterprism, great-rhombated-icositetrachoron atop alternate great-rhombated-icositetrachoron
Circumradius	sqrt[39+25 sqrt(2)]/2 = 4.311477
Face vector	1152, 3456, 3744, 1680, 242
Confer	general polytopal classes: segmentotera   scaliform
External links

Incidence matrix according to Dynkin symbol

xo3xx4xx3ox&#x   → height = sqrt[sqrt(2)-1] = 0.643594
(grico || alt. grico)

o.3o.4o.3o.    & | 1152 |   1   1    2    2 |   1   2   2   1    3    4 |  2   1  1   3   3   1   2 | 1  3   2
-----------------+------+-------------------+---------------------------+---------------------------+---------
x. .. .. ..    & |    2 | 576   *    *    * |   1   2   0   0    2    0 |  2   1  0   2   2   1   0 | 1  2   2
.. x. .. ..    & |    2 |   * 576    *    * |   1   0   2   0    0    2 |  2   0  1   2   1   0   2 | 1  3   1
.. .. 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.3x. .. ..    & |    6 |   3   3    0    0 | 192   *   *   *    *    * |  2   0  0   2   0   0   0 | 1  2   1
x. .. x. ..    & |    4 |   2   0    2    0 |   * 576   *   *    *    * |  1   1  0   0   1   0   0 | 1  1   1
.. x.4x. ..    & |    8 |   0   4    4    0 |   *   * 288   *    *    * |  1   0  1   0   0   0   1 | 1  2   0
.. .. x.3o.    & |    3 |   0   0    3    0 |   *   *   * 384    *    * |  0   1  1   1   0   0   0 | 1  1   1
xo .. .. ..&#x & |    3 |   1   0    0    2 |   *   *   *   * 1152    * |  0   0  0   1   1   1   0 | 0  1   2
.. xx .. ..&#x & |    4 |   0   1    1    2 |   *   *   *   *    * 1152 |  0   0  0   1   1   0   1 | 0  2   1
-----------------+------+-------------------+---------------------------+---------------------------+---------
x.3x.4x. ..    & ♦   48 |  24  24   24    0 |   8  12   6   0    0    0 | 48   *  *   *   *   *   * | 1  1   0
x. .. x.3o.    & ♦    6 |   3   0    6    0 |   0   3   0   2    0    0 |  * 192  *   *   *   *   * | 1  0   1
.. x.4x.3o.    & ♦   24 |   0  12   24    0 |   0   0   6   8    0    0 |  *   * 48   *   *   *   * | 1  1   0
xo3xx .. ..&#x & ♦    9 |   3   3    3    6 |   1   0   0   1    3    3 |  *   *  * 384   *   *   * | 0  1   1
xo .. xx ..&#x & ♦    6 |   2   1    2    4 |   0   1   0   0    2    2 |  *   *  *   * 576   *   * | 0  1   1
xo .. .. ox&#x   ♦    4 |   2   0    0    4 |   0   0   0   0    4    0 |  *   *  *   *   * 288   * | 0  0   2
.. xx4xx ..&#x   ♦   16 |   0   8    8    8 |   0   0   2   0    0    8 |  *   *  *   *   *   * 144 | 0  2   0
-----------------+------+-------------------+---------------------------+---------------------------+---------
x.3x.4x.3o.    & ♦  576 | 288 288  576    0 |  96 288 144 192    0    0 | 24  96 24   0   0   0   0 | 2  *   *
xo3xx4xx ..&#x & ♦   72 |  24  36   48   48 |   8  12  12   8   24   48 |  1   0  1   8  12   0   6 | * 48   *
xo3xx .. ox&#x & ♦   12 |   6   3    6   12 |   1   3   0   2   12    6 |  0   1  0   2   3   3   0 | *  * 192