No uniform realisation is possible. It occurs as faceting of the truncation of the small stellated dodecahedron (3doe).

Incidence matrix according to Dynkin symbol

x5/2β5o

both( .   . . ) | 60 |  1  2  2 |  2  1  2
----------------+----+----------+------
both( x   . . ) |  2 | 30  *  * |  2  0  0
sefa( x5/2β . ) |  2 |  * 60  * |  1  0  1
sefa( .   β5o ) |  2 |  *  * 60 |  0  1  1
----------------+----+----------+------
      x5/2β .   ♦ 10 |  5  5  0 | 12  *  *
          β5o   ♦  5 |  0  0  5 |  * 12  *
sefa( x5/2β5o ) |  4 |  0  2  2 |  *  * 30

starting figure: x5/2x5o