No uniform realisation is possible.

Incidence matrix according to Dynkin symbol

β3β3β5x

both( . . . . ) | 14400 |    1    1     2     2    1 |    1    1    1     3    2    2    2 |    1    1   1   1    3
----------------+-------+----------------------------+-------------------------------------+-----------------------
both( . . . x ) |     2 | 7200    *     *     *    * |    0    0    1     0    2    1    1 |    0    1   1   1    2
both( s 2 s . ) |     2 |    * 7200     *     *    * |    0    0    0     2    0    2    0 |    1    0   1   0    2
sefa( s3s . . ) |     2 |    *    * 14400     *    * |    1    0    0     1    1    0    0 |    1    1   0   0    1
sefa( . s3s . ) |     2 |    *    *     * 14400    * |    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
----------------+-------+----------------------------+-------------------------------------+-----------------------
both( s3s . . ) ♦     3 |    0    0     3     0    0 | 4800    *    *     *    *    *    * |    1    1   0   0    0
both( . s3s . ) ♦     3 |    0    0     0     3    0 |    * 4800    *     *    *    *    * |    1    0   0   1    0
      . . β5x   ♦    10 |    5    0     0     0    5 |    *    * 1440     *    *    *    * |    0    0   1   1    0
sefa( s3s3s . ) |     3 |    0    1     1     1    0 |    *    *    * 14400    *    *    * |    1    0   0   0    1
sefa( s3s 2 x ) |     4 |    2    0     2     0    0 |    *    *    *     * 7200    *    * |    0    1   0   0    1
sefa( β 2 β5x ) |     4 |    1    2     0     0    1 |    *    *    *     *    * 7200    * |    0    0   1   0    1
sefa( . β3β5x ) |     4 |    1    0     0     2    1 |    *    *    *     *    *    * 7200 |    0    0   0   1    1
----------------+-------+----------------------------+-------------------------------------+-----------------------
both( s3s3s . ) ♦    12 |    0    6    12    12    0 |    4    4    0    12    0    0    0 | 1200    *   *   *    *
both( s3s 2 x ) ♦     6 |    3    0     6     0    0 |    2    0    0     0    3    0    0 |    * 2400   *   *    *
      β 2 β5x   ♦    20 |   10   10     0     0   10 |    0    0    2     0    0   10    0 |    *    * 720   *    *
      . β3β5x   ♦   120 |   60    0     0   120   60 |    0   40   12     0    0    0   60 |    *    *   * 120    *
sefa( β3β3β5x ) ♦     6 |    2    2     2     2    1 |    0    0    0     2    1    1    1 |    *    *   *   * 7200

starting figure: x3x3x5x