No uniform realisation is possible.

Incidence matrix according to Dynkin symbol

x3β3x5β

both( . . . . ) | 14400 |    1    1    1    1    1    1 |    1    1    1    1    1    2    1    2 |   1    1   1   1    2
----------------+-------+-------------------------------+-----------------------------------------+----------------------
both( x . . . ) |     2 | 7200    *    *    *    *    * |    1    1    0    0    0    1    1    0 |   1    1   1   0    1
both( . . x . ) |     2 |    * 7200    *    *    *    * |    1    0    1    1    0    0    0    0 |   1    0   1   1    0
both( . s 2 s ) |     2 |    *    * 7200    *    *    * |    0    0    0    0    0    2    0    2 |   0    1   0   1    2
sefa( x3β . . ) |     2 |    *    *    * 7200    *    * |    0    1    0    0    1    1    0    0 |   1    1   0   0    1
sefa( . β3x . ) |     2 |    *    *    *    * 7200    * |    0    0    1    0    1    0    0    1 |   1    0   0   1    1
sefa( . . x5β ) |     2 |    *    *    *    *    * 7200 |    0    0    0    1    0    0    1    1 |   0    0   1   1    1
----------------+-------+-------------------------------+-----------------------------------------+----------------------
both( x . x . ) |     4 |    2    2    0    0    0    0 | 3600    *    *    *    *    *    *    * |   1    0   1   0    0
      x3β . .   ♦     6 |    3    0    0    3    0    0 |    * 2400    *    *    *    *    *    * |   1    1   0   0    0
      . β3x .   ♦     6 |    0    3    0    0    3    0 |    *    * 2400    *    *    *    *    * |   1    0   0   1    0
      . . x5β   ♦    10 |    0    5    0    0    0    5 |    *    *    * 1440    *    *    *    * |   0    0   1   1    0
sefa( x3β3x . ) |     4 |    0    0    0    2    2    0 |    *    *    *    * 3600    *    *    * |   1    0   0   0    1
sefa( x3β 2 β ) |     4 |    1    0    2    1    0    0 |    *    *    *    *    * 7200    *    * |   0    1   0   0    1
sefa( x 2 x5β ) |     4 |    2    0    0    0    0    2 |    *    *    *    *    *    * 3600    * |   0    0   1   0    1
sefa( . β3x5β ) |     4 |    0    0    2    0    1    1 |    *    *    *    *    *    *    * 7200 |   0    0   0   1    1
----------------+-------+-------------------------------+-----------------------------------------+----------------------
      x3β3x .   ♦    24 |   12   12    0   12   12    0 |    6    4    4    0    6    0    0    0 | 600    *   *   *    *
      x3β 2 β   ♦    12 |    6    0    6    6    0    0 |    0    2    0    0    0    6    0    0 |   * 1200   *   *    *
      x 2 x5β   ♦    20 |   10   10    0    0    0   10 |    5    0    0    2    0    0    5    0 |   *    * 720   *    *
      . β3x5β   ♦   120 |    0   60   60    0   60   60 |    0    0   20   12    0    0    0   60 |   *    *   * 120    *
sefa( x3β3x5β ) ♦     8 |    2    0    4    2    2    2 |    0    0    0    0    1    2    1    2 |   *    *   *   * 3600

starting figure: x3x3x5x