⭳

Looks like a compound of 2 cuboctahedra (co) plus 16 pairs of coincident {3}. And indeed vertices and {4} coincide by pairs, edges coincide by 3, and each {3/2} coincides with 3 {3}.

Incidence matrix according to Dynkin symbol

β4β3o

both( . . .    ) | 24 |  2  2  2 | 1 1 1  3
-----------------+----+----------+---------
sefa( s4s . (r)) |  2 | 24  *  * | 1 0 0  1
sefa( s4s . (l)) |  2 |  * 24  * | 0 1 0  1
sefa( . β3o    ) |  2 |  *  * 24 | 0 0 1  1
-----------------+----+----------+---------
      s4s . (r)  ♦  4 |  4  0  0 | 6 * *  *
      s4s . (l)  ♦  4 |  0  4  0 | * 6 *  *
      . β3o      ♦  3 |  0  0  3 | * * 8  *
sefa( β4β3o    ) |  3 |  1  1  1 | * * * 24

or
both( . . . ) | 24 |  4  2 |  2 1  3
--------------+----+-------+--------
sefa( s4s . ) |  2 | 48  * |  1 0  1
sefa( . β3o ) |  2 |  * 24 |  0 1  1
--------------+----+-------+--------
both( s4s . ) ♦  4 |  4  0 | 12 *  *
      . β3o   ♦  3 |  0  3 |  * 8  *
sefa( β4β3o ) |  3 |  2  1 |  * * 24

starting figure: x4x3o