Looks like a compound of 4 coincident pentachora (pen). Indeed vertices and edges come in coincident quadruples, faces are coincident as one {6/2} and two triangles each, and cells are coincident as one tet and three 3tets.

Incidence matrix according to Dynkin symbol

x3/2x3o3o

.   . . . | 20 ♦  1  3 |  3  3 | 3 1
----------+----+-------+-------+----
x   . . . |  2 | 10  * |  3  0 | 3 0
.   x . . |  2 |  * 30 |  1  2 | 2 1
----------+----+-------+-------+----
x3/2x . . |  6 |  3  3 | 10  * | 2 0  {6/2}
.   x3o . |  3 |  0  3 |  * 20 | 1 1
----------+----+-------+-------+----
x3/2x3o . ♦ 12 |  6 12 |  4  4 | 5 *
.   x3o3o ♦  4 |  0  6 |  0  4 | * 5

x3/2x3/2o3o

.   .   . . | 20 ♦  1  3 |  3  3 | 3 1
------------+----+-------+-------+----
x   .   . . |  2 | 10  * |  3  0 | 3 0
.   x   . . |  2 |  * 30 |  1  2 | 2 1
------------+----+-------+-------+----
x3/2x   . . |  6 |  3  3 | 10  * | 2 0  {6/2}
.   x3/2o . |  3 |  0  3 |  * 20 | 1 1
------------+----+-------+-------+----
x3/2x3/2o . ♦ 12 |  6 12 |  4  4 | 5 *
.   x3/2o3o ♦  4 |  0  6 |  0  4 | * 5

x3/2x3o3/2o

.   . .   . | 20 ♦  1  3 |  3  3 | 3 1
------------+----+-------+-------+----
x   . .   . |  2 | 10  * |  3  0 | 3 0
.   x .   . |  2 |  * 30 |  1  2 | 2 1
------------+----+-------+-------+----
x3/2x .   . |  6 |  3  3 | 10  * | 2 0  {6/2}
.   x3o   . |  3 |  0  3 |  * 20 | 1 1
------------+----+-------+-------+----
x3/2x3o   . ♦ 12 |  6 12 |  4  4 | 5 *
.   x3o3/2o ♦  4 |  0  6 |  0  4 | * 5

x3/2x3/2o3/2o

.   .   .   . | 20 ♦  1  3 |  3  3 | 3 1
--------------+----+-------+-------+----
x   .   .   . |  2 | 10  * |  3  0 | 3 0
.   x   .   . |  2 |  * 30 |  1  2 | 2 1
--------------+----+-------+-------+----
x3/2x   .   . |  6 |  3  3 | 10  * | 2 0  {6/2}
.   x3/2o   . |  3 |  0  3 |  * 20 | 1 1
--------------+----+-------+-------+----
x3/2x3/2o   . ♦ 12 |  6 12 |  4  4 | 5 *
.   x3/2o3/2o ♦  4 |  0  6 |  0  4 | * 5