No uniform realisation is possible.

Incidence matrix according to Dynkin symbol

β3o3β5x

both( . . . . ) | 7200 |    1    2    2    2    2 |    1    1    2    4    2    4    2 |   1    1   2   1    4
----------------+------+--------------------------+------------------------------------+----------------------
both( . . . x ) |    2 | 3600    *    *    *    * |    0    0    2    0    2    2    0 |   0    1   2   1    2
both( s 2 s . ) |    2 |    * 7200    *    *    * |    0    0    0    2    0    2    0 |   1    0   1   0    2
sefa( β3o . . ) |    2 |    *    * 7200    *    * |    1    0    0    1    1    0    0 |   1    1   0   0    1
sefa( . o3β . ) |    2 |    *    *    * 7200    * |    0    1    0    1    0    0    1 |   1    0   0   1    1
sefa( . . β5x ) |    2 |    *    *    *    * 7200 |    0    0    1    0    0    1    1 |   0    0   1   1    1
----------------+------+--------------------------+------------------------------------+----------------------
      β3o . .   ♦    3 |    0    0    3    0    0 | 2400    *    *    *    *    *    * |   1    1   0   0    0
      . o3β .   ♦    3 |    0    0    0    3    0 |    * 2400    *    *    *    *    * |   1    0   0   1    0
      . . β5x   ♦   10 |    5    0    0    0    5 |    *    * 1440    *    *    *    * |   0    0   1   1    0
sefa( β3o3β . ) |    4 |    0    2    1    1    0 |    *    *    * 7200    *    *    * |   1    0   0   0    1
sefa( β3o 2 x ) |    4 |    2    0    2    0    0 |    *    *    *    * 3600    *    * |   0    1   0   0    1
sefa( β 2 β5x ) |    4 |    1    2    0    0    1 |    *    *    *    *    * 7200    * |   0    0   1   0    1
sefa( . o3β5x ) |    4 |    0    0    0    2    2 |    *    *    *    *    *    * 3600 |   0    0   0   1    1
----------------+------+--------------------------+------------------------------------+----------------------
      β3o3β .   ♦   12 |    0   12   12   12    0 |    4    4    0   12    0    0    0 | 600    *   *   *    *
      β3o 2 x   ♦    6 |    3    0    6    0    0 |    2    0    0    0    3    0    0 |   * 1200   *   *    *
      β 2 β5x   ♦   20 |   10   10    0    0   10 |    0    0    2    0    0   10    0 |   *    * 720   *    *
      . o3β5x   ♦   60 |   30    0    0   60   60 |    0   20   12    0    0    0   30 |   *    *   * 120    *
sefa( β3o3β5x ) ♦    8 |    2    4    2    2    2 |    0    0    0    2    1    2    1 |   *    *   *   * 3600

starting figure: x3o3x5x