No uniform realisation is possible.

Incidence matrix according to Dynkin symbol

x3β3β5x

both( . . . . ) | 14400 |    1    1    1     2    1 |    1    1    1    1    2    1    1    2 |   1    1   1   1    2
----------------+-------+---------------------------+-----------------------------------------+----------------------
both( x . . . ) |     2 | 7200    *    *     *    * |    1    1    0    0    1    0    1    0 |   1    1   1   0    1
both( . . . x ) |     2 |    * 7200    *     *    * |    1    0    0    1    0    1    0    1 |   0    1   1   1    1
sefa( x3β . . ) |     2 |    *    * 7200     *    * |    0    1    0    0    1    1    0    0 |   1    1   0   0    1
sefa( . s3s . ) |     2 |    *    *    * 14400    * |    0    0    1    0    1    0    0    1 |   1    0   0   1    1
sefa( . . β5x ) |     2 |    *    *    *     * 7200 |    0    0    0    1    0    0    1    1 |   0    0   1   1    1
----------------+-------+---------------------------+-----------------------------------------+----------------------
both( x . . x ) |     4 |    2    2    0     0    0 | 3600    *    *    *    *    *    *    * |   0    1   1   0    0
      x3β . .   ♦     6 |    3    0    3     0    0 |    * 2400    *    *    *    *    *    * |   1    1   0   0    0
both( . s3s . ) ♦     3 |    0    0    0     3    0 |    *    * 4800    *    *    *    *    * |   1    0   0   1    0
      . . β5x   ♦    10 |    0    5    0     0    5 |    *    *    * 1440    *    *    *    * |   0    0   1   1    0
sefa( x3β3β . ) |     4 |    1    0    1     2    0 |    *    *    *    * 7200    *    *    * |   1    0   0   0    1
sefa( x3β 2 x ) |     4 |    0    2    2     0    0 |    *    *    *    *    * 3600    *    * |   0    1   0   0    1
sefa( x 2 β5x ) |     4 |    2    0    0     0    2 |    *    *    *    *    *    * 3600    * |   0    0   1   0    1
sefa( . β3β5x ) |     4 |    0    1    0     2    1 |    *    *    *    *    *    *    * 7200 |   0    0   0   1    1
----------------+-------+---------------------------+-----------------------------------------+----------------------
      x3β3β .   ♦    24 |   12    0   12    24    0 |    0    4    8    0   12    0    0    0 | 600    *   *   *    *
      x3β 2 x   ♦    12 |    6    6    6     0    0 |    3    2    0    0    0    3    0    0 |   * 1200   *   *    *
      x 2 β5x   ♦    20 |   10   10    0     0   10 |    5    0    0    2    0    0    5    0 |   *    * 720   *    *
      . β3β5x   ♦   120 |    0   60    0   120   60 |    0    0   40   12    0    0    0   60 |   *    *   * 120    *
sefa( x3β3β5x ) ♦     8 |    2    2    2     4    2 |    0    0    0    0    2    1    1    2 |   *    *   *   * 3600

starting figure: x3x3x5x