No uniform realisation is possible.

Incidence matrix according to Dynkin symbol

β3β3x3β

both( . . . .    ) | 120 |  1  1  1   2  1  1 |  1  1  1  2   3  2  2 | 1  1  1 1  3
-------------------+-----+--------------------+-----------------------+-------------
both( . . x .    ) |   2 | 60  *  *   *  *  * |  0  1  1  1   0  1  0 | 1  0  1 1  1
both( s . . s2*a ) |   2 |  * 60  *   *  *  * |  0  0  0  0   2  2  0 | 0  1  1 0  2
both( . s 2 s    ) |   2 |  *  * 60   *  *  * |  0  0  0  0   2  0  2 | 0  1  0 1  2
sefa( s3s . .    ) |   2 |  *  *  * 120  *  * |  1  0  0  1   1  0  0 | 1  1  0 0  1
sefa( . β3x .    ) |   2 |  *  *  *   * 60  * |  0  1  0  1   0  0  1 | 1  0  0 1  1
sefa( . . x3β    ) |   2 |  *  *  *   *  * 60 |  0  0  1  0   0  1  1 | 0  0  1 1  1
-------------------+-----+--------------------+-----------------------+-------------
both( s3s . .    ) ♦   3 |  0  0  0   3  0  0 | 40  *  *  *   *  *  * | 1  1  0 0  0
      . β3x .      ♦   6 |  3  0  0   0  3  0 |  * 20  *  *   *  *  * | 1  0  0 1  0
      . . x3β      ♦   6 |  3  0  0   0  0  3 |  *  * 20  *   *  *  * | 0  0  1 1  0
sefa( β3β3x .    ) |   4 |  1  0  0   2  1  0 |  *  *  * 60   *  *  * | 1  0  0 0  1
sefa( s3s . s2*a ) |   3 |  0  1  1   1  0  0 |  *  *  *  * 120  *  * | 0  1  0 0  1
sefa( β . x3β2*a ) |   4 |  1  2  0   0  0  1 |  *  *  *  *   * 60  * | 0  0  1 0  1
sefa( . β3x3β    ) |   4 |  0  0  2   0  1  1 |  *  *  *  *   *  * 60 | 0  0  0 1  1
-------------------+-----+--------------------+-----------------------+-------------
both( β3β3x .    ) ♦  24 | 12  0  0  24 12  0 |  8  4  0 12   0  0  0 | 5  *  * *  *
both( s3s . s2*a ) ♦   6 |  0  3  3   6  0  0 |  2  0  0  0   6  0  0 | * 20  * *  *
      β . x3β2*a   ♦  12 |  6  6  0   0  0  6 |  0  0  2  0   0  6  0 | *  * 10 *  *
      . β3x3β      ♦  24 | 12  0 12   0 12 12 |  0  4  4  0   0  0 12 | *  *  * 5  *
sefa( β3β3x3β    ) ♦   6 |  1  2  2   2  1  1 |  0  0  0  1   2  1  1 | *  *  * * 60

starting figure: x3x3x3x