Looks like a compound of a rectified pentachoron (rap) and a facetted rectified pentachoron (firp) with vertices identified and squares coincidently doubled up.

Incidence matrix according to Dynkin symbol

o3β3o3o

both( . . . . ) | 10 |  6 12 |  3  6 12  6 | 3 2  6
----------------+----+-------+-------------+-------
sefa( o3β . . ) |  2 | 30  * |  1  0  2  0 | 2 0  1
sefa( . β3o . ) |  2 |  * 60 |  0  1  1  1 | 1 1  1
----------------+----+-------+-------------+-------
      o3β . .   ♦  3 |  3  0 | 10  *  *  * | 2 0  0
      . β3o .   ♦  3 |  0  3 |  * 20  *  * | 1 1  0
sefa( o3β3o . ) |  4 |  2  2 |  *  * 30  * | 1 0  1
sefa( . β3o3o ) |  3 |  0  3 |  *  *  * 20 | 0 1  1
----------------+----+-------+-------------+-------
      o3β3o .   ♦  6 | 12 12 |  4  4  6  0 | 5 *  *
      . β3o3o   ♦  4 |  0 12 |  0  4  0  4 | * 5  *
sefa( o3β3o3o ) ♦  6 |  3  6 |  0  0  3  2 | * * 10

starting figure: o3x3o3o