No uniform realisation is possible.

Incidence matrix according to Dynkin symbol

β3x3β3o

both( . . . . ) | 60 |  1  2  1  2  2 |  1  2  1  4  3  2 | 2  1 1  3
----------------+----+----------------+-------------------+----------
both( . x . . ) |  2 | 30  *  *  *  * |  1  2  0  0  0  0 | 2  0 1  0
both( s 2 s . ) |  2 |  * 60  *  *  * |  0  0  0  2  2  0 | 1  1 0  2
sefa( β3x . . ) |  2 |  *  * 30  *  * |  1  0  0  2  0  0 | 2  0 0  1
sefa( . x3β . ) |  2 |  *  *  * 60  * |  0  1  0  1  0  1 | 1  0 1  1
sefa( . . β3o ) |  2 |  *  *  *  * 60 |  0  0  1  0  1  1 | 0  1 1  1
----------------+----+----------------+-------------------+----------
      β3x . .   ♦  6 |  3  0  3  0  0 | 10  *  *  *  *  * | 2  0 0  0
      . x3β .   ♦  6 |  3  0  0  3  0 |  * 20  *  *  *  * | 1  0 1  0
      . . β3o   ♦  3 |  0  0  0  0  3 |  *  * 20  *  *  * | 0  1 1  0
sefa( β3x3β . ) |  4 |  0  2  1  1  0 |  *  *  * 60  *  * | 1  0 0  1
sefa( β 2 β3o ) |  3 |  0  2  0  0  1 |  *  *  *  * 60  * | 0  1 0  1
sefa( . x3β3o ) |  4 |  0  0  0  2  2 |  *  *  *  *  * 30 | 0  0 1  1
----------------+----+----------------+-------------------+----------
      β3x3β     ♦ 24 | 12 12 12 12  0 |  4  4  0 12  0  0 | 5  * *  *
      β 2 β3o   ♦  6 |  0  6  0  0  6 |  0  0  2  0  6  0 | * 10 *  *
      . x3β3o   ♦ 12 |  6  0  0 12 12 |  0  4  4  0  0  6 | *  * 5  *
sefa( β3x3β3o ) ♦  6 |  0  4  1  2  2 |  0  0  0  2  2  1 | *  * * 30

starting figure: x3x3x3o