No uniform realisation is possible.

Incidence matrix according to Dynkin symbol

β3x3β3x

both( . . . . ) | 120 |  1  1  1  1  1  1 |  1  1  1  1  2  1  2  1 | 1  1  1 1  2
----------------+-----+-------------------+-------------------------+-------------
both( . x . . ) |   2 | 60  *  *  *  *  * |  1  1  1  0  0  0  0  0 | 1  1  0 1  0
both( . . . x ) |   2 |  * 60  *  *  *  * |  1  0  0  1  0  1  1  0 | 0  1  1 1  1
both( s 2 s . ) |   2 |  *  * 60  *  *  * |  0  0  0  0  2  0  2  0 | 1  0  1 0  2
sefa( β3x . . ) |   2 |  *  *  * 60  *  * |  0  1  0  0  1  1  0  0 | 1  1  0 0  1
sefa( . x3β . ) |   2 |  *  *  *  * 60  * |  0  0  1  0  1  0  0  1 | 1  0  0 1  1
sefa( . . β3x ) |   2 |  *  *  *  *  * 60 |  0  0  0  1  0  0  1  1 | 0  0  1 1  1
----------------+-----+-------------------+-------------------------+-------------
both( . x . x ) |   4 |  2  2  0  0  0  0 | 30  *  *  *  *  *  *  * | 0  1  0 1  0
      β3x . .   ♦   6 |  3  0  0  3  0  0 |  * 20  *  *  *  *  *  * | 1  1  0 0  0
      . x3β .   ♦   6 |  3  0  0  0  3  0 |  *  * 20  *  *  *  *  * | 1  0  0 1  0
      . . β3x   ♦   6 |  0  3  0  0  0  3 |  *  *  * 20  *  *  *  * | 0  0  1 1  0
sefa( β3x3β . ) |   4 |  0  0  2  1  1  0 |  *  *  *  * 60  *  *  * | 1  0  0 0  1
sefa( β3x . x ) |   4 |  0  2  0  2  0  0 |  *  *  *  *  * 30  *  * | 0  1  0 0  1
sefa( β 2 β3x ) |   4 |  0  1  2  0  0  1 |  *  *  *  *  *  * 60  * | 0  0  1 0  1
sefa( . x3β3x ) |   4 |  0  0  0  0  2  2 |  *  *  *  *  *  *  * 30 | 0  0  0 1  1
----------------+-----+-------------------+-------------------------+-------------
      β3x3β .   ♦  24 | 12  0 12 12 12  0 |  0  4  4  0 12  0  0  0 | 5  *  * *  *
      β3x . x   ♦  12 |  6  6  0  6  0  0 |  3  2  0  0  0  3  0  0 | * 10  * *  *
      β 2 β3x   ♦  12 |  0  6  6  0  0  6 |  0  0  0  2  0  0  6  0 | *  * 10 *  *
      . x3β3x   ♦  24 | 12 12  0  0 12 12 |  6  0  4  4  0  0  0  6 | *  *  * 5  *
sefa( β3x3β3x ) ♦   8 |  0  2  4  2  2  2 |  0  0  0  0  2  1  2  1 | *  *  * * 20

starting figure: x3x3x3x