No uniform realisation is possible.

Incidence matrix according to Dynkin symbol

β3o3β5o

both( . . . . ) | 3600 |    4    2    4    4 |    1    2    2    8    8    4 |   2   2   1    6
----------------+------+---------------------+-------------------------------+-----------------
both( s 2 s . ) |    2 | 7200    *    *    * |    0    0    0    2    2    0 |   1   1   0    2
sefa( β3o . . ) |    2 |    * 3600    *    * |    1    0    0    2    0    0 |   2   0   0    1
sefa( . o3β . ) |    2 |    *    * 7200    * |    0    1    0    1    0    1 |   1   0   1    1
sefa( . . β5o ) |    2 |    *    *    * 7200 |    0    0    1    0    1    1 |   0   1   1    1
----------------+------+---------------------+-------------------------------+-----------------
      β3o . .   ♦    3 |    0    3    0    0 | 1200    *    *    *    *    * |   2   0   0    0
      . o3β .   ♦    3 |    0    0    3    0 |    * 2400    *    *    *    * |   1   0   1    0
      . . β5o   ♦    5 |    0    0    0    5 |    *    * 1440    *    *    * |   0   1   1    0
sefa( β3o3β . ) |    4 |    2    1    1    0 |    *    *    * 7200    *    * |   1   0   0    1
sefa( β 2 β5o ) |    3 |    2    0    0    1 |    *    *    *    * 7200    * |   0   1   0    1
sefa( . o3β5o ) |    4 |    0    0    2    2 |    *    *    *    *    * 3600 |   0   0   1    1
----------------+------+---------------------+-------------------------------+-----------------
      β3o3β .   ♦   12 |   12   12   12    0 |    4    4    0   12    0    0 | 600   *   *    *
      β 2 β5o   ♦   10 |   10    0    0   10 |    0    0    2    0   10    0 |   * 720   *    *
      . o3β5o   ♦   30 |    0    0   60   60 |    0   20   12    0    0   30 |   *   * 120    *
sefa( β3o3β5o ) ♦    6 |    4    1    2    2 |    0    0    0    2    2    1 |   *   *   * 3600

starting figure: x3o3x5o