No uniform realisation is possible. It occurs as faceting of the small rhombicosidodecahedron (srid).

Incidence matrix according to Dynkin symbol

β3o5β

both( . . . ) | 60 |  2  2  2 |  1  1  4
--------------+----+----------+---------
both( s 2 s ) |  2 | 60  *  * |  0  0  2  q
sefa( β3o . ) |  2 |  * 60  * |  1  0  1  x
sefa( . o5β ) |  2 |  *  * 60 |  0  1  1  f
--------------+----+----------+---------
      β3o .   ♦  3 |  0  3  0 | 20  *  *
      . o5β   ♦  5 |  0  0  5 |  * 12  *
sefa( β3o5β ) |  4 |  2  1  1 |  *  * 60

starting figure: x3o5x