No uniform realisation is possible. It occurs as faceting of the great rhombicosidodecahedron (grid).

Incidence matrix according to Dynkin symbol

β3x5β

both( . . . ) | 120 |  1  1  1  1 |  1  1  2
--------------+-----+-------------+---------
both( . x . ) |   2 | 60  *  *  * |  1  1  0
both( s 2 s ) |   2 |  * 60  *  * |  0  0  2
sefa( β3x . ) |   2 |  *  * 60  * |  1  0  1
sefa( . x5β ) |   2 |  *  *  * 60 |  0  1  1
--------------+-----+-------------+---------
      β3x .   ♦   6 |  3  0  3  0 | 20  *  *
      . x5β   ♦  10 |  5  0  0  5 |  * 12  *
sefa( β3x5β ) |   4 |  0  2  1  1 |  *  * 60

starting figure: x3x5x