Looks like a compound of a prismatopentaintercepted dispentachoron (pinnipdip) plus 15 additional squares which are coincident to one class of those of pinnipdip. Edges are to be doubled up along with, while vertices are identified.

Incidence matrix according to Dynkin symbol

x3o3β3o

both( . . . . ) | 30 |  2  4  4 |  1  2  2  4  4  4 | 2  2 1  4
----------------+----+----------+-------------------+----------
both( x . . . ) |  2 | 30  *  * |  1  0  0  2  2  0 | 2  1 0  2
sefa( . o3β . ) |  2 |  * 60  * |  0  1  0  1  0  1 | 1  0 1  1
sefa( . . β3o ) |  2 |  *  * 60 |  0  0  1  0  1  1 | 0  1 1  1
----------------+----+----------+-------------------+----------
both( x3o . . ) |  3 |  3  0  0 | 10  *  *  *  *  * | 2  0 0  0
      . o3β .   ♦  3 |  0  3  0 |  * 20  *  *  *  * | 1  0 1  0
      . . β3o   ♦  3 |  0  0  3 |  *  * 20  *  *  * | 0  1 1  0
sefa( x3o3β . ) |  6 |  3  3  0 |  *  *  * 20  *  * | 1  0 0  1
sefa( x . β3o ) |  4 |  2  0  2 |  *  *  *  * 30  * | 0  1 0  1
sefa( . o3β3o ) |  4 |  0  2  2 |  *  *  *  *  * 30 | 0  0 1  1
----------------+----+----------+-------------------+----------
      x3o3β .   ♦ 12 | 12 12  0 |  4  4  0  4  0  0 | 5  * *  *
      x . β3o   ♦  6 |  3  0  6 |  0  0  2  0  3  0 | * 10 *  *
      . o3β3o   ♦  6 |  0 12 12 |  0  4  4  0  0  6 | *  * 5  *
sefa( x3o3β3o ) ♦ 12 |  6  6  6 |  0  0  0  2  3  3 | *  * * 10

starting figure: x3o3x3o