Looks like a compound of 4 coincident hecatonicosachora (hi). Indeed vertices and edges come in coincident quadruples, faces are coincident as one {10/2} and two pentagons each, and cells are coincident as one doe and three 3does.

Incidence matrix according to Dynkin symbol

o3o5x5/2x

. . .   . | 2400 ♦    3    1 |    3   3 |   1   3
----------+------+-----------+----------+--------
. . x   . |    2 | 3600    * |    2   1 |   1   2
. . .   x |    2 |    * 1200 |    0   3 |   0   3
----------+------+-----------+----------+--------
. o5x   . |    5 |    5    0 | 1440   * |   1   1
. . x5/2x |   10 |    5    5 |    * 720 |   0   2
----------+------+-----------+----------+--------
o3o5x   . ♦   20 |   30    0 |   12   0 | 120   *
. o5x5/2x ♦   60 |   60   30 |   12  12 |   * 120

o3/2o5x5/2x

.   . .   . | 2400 ♦    3    1 |    3   3 |   1   3
------------+------+-----------+----------+--------
.   . x   . |    2 | 3600    * |    2   1 |   1   2
.   . .   x |    2 |    * 1200 |    0   3 |   0   3
------------+------+-----------+----------+--------
.   o5x   . |    5 |    5    0 | 1440   * |   1   1
.   . x5/2x |   10 |    5    5 |    * 720 |   0   2
------------+------+-----------+----------+--------
o3/2o5x   . ♦   20 |   30    0 |   12   0 | 120   *
.   o5x5/2x ♦   60 |   60   30 |   12  12 |   * 120

o3o5/4x5/2x

. .   .   . | 2400 ♦    3    1 |    3   3 |   1   3
------------+------+-----------+----------+--------
. .   x   . |    2 | 3600    * |    2   1 |   1   2
. .   .   x |    2 |    * 1200 |    0   3 |   0   3
------------+------+-----------+----------+--------
. o5/4x   . |    5 |    5    0 | 1440   * |   1   1
. .   x5/2x |   10 |    5    5 |    * 720 |   0   2
------------+------+-----------+----------+--------
o3o5/4x   . ♦   20 |   30    0 |   12   0 | 120   *
. o5/4x5/2x ♦   60 |   60   30 |   12  12 |   * 120

o3/2o5/4x5/2x

.   .   .   . | 2400 ♦    3    1 |    3   3 |   1   3
--------------+------+-----------+----------+--------
.   .   x   . |    2 | 3600    * |    2   1 |   1   2
.   .   .   x |    2 |    * 1200 |    0   3 |   0   3
--------------+------+-----------+----------+--------
.   o5/4x   . |    5 |    5    0 | 1440   * |   1   1
.   .   x5/2x |   10 |    5    5 |    * 720 |   0   2
--------------+------+-----------+----------+--------
o3/2o5/4x   . ♦   20 |   30    0 |   12   0 | 120   *
.   o5/4x5/2x ♦   60 |   60   30 |   12  12 |   * 120