No uniform realisation is possible.

Incidence matrix according to Dynkin symbol

β3β3β3o

both( . . . . ) | 60 |  2  2   4  2 |  1  2  1   6  3  3 |  2  1 1  4
----------------+----+--------------+--------------------+-----------
both( s 2 s . ) |  2 | 60  *   *  * |  0  0  0   2  2  0 |  1  1 0  2
sefa( s3s . . ) |  2 |  * 60   *  * |  1  0  0   2  0  0 |  2  0 0  1
sefa( . s3s . ) |  2 |  *  * 120  * |  0  1  0   1  0  1 |  1  0 1  1
sefa( . . β3o ) |  2 |  *  *   * 60 |  0  0  1   0  1  1 |  0  1 1  1
----------------+----+--------------+--------------------+-----------
both( s3s . . ) ♦  3 |  0  3   0  0 | 20  *  *   *  *  * |  2  0 0  0
both( . s3s . ) ♦  3 |  0  0   3  0 |  * 40  *   *  *  * |  1  0 1  0
      . . β3o   ♦  3 |  0  0   0  3 |  *  * 20   *  *  * |  0  1 1  0
sefa( s3s3s . ) |  3 |  1  1   1  0 |  *  *  * 120  *  * |  1  0 0  1
sefa( β 2 β3o ) |  3 |  2  0   0  1 |  *  *  *   * 60  * |  0  1 0  1
sefa( . β3β3o ) |  3 |  0  0   2  1 |  *  *  *   *  * 60 |  0  0 1  1
----------------+----+--------------+--------------------+-----------
both( s3s3s . ) ♦ 12 |  6 12  12  0 |  4  4  0  12  0  0 | 10  * *  *
      β 2 β3o   ♦  6 |  6  0   0  6 |  0  0  2   0  6  0 |  * 10 *  *
      . β3β3o   ♦ 12 |  0  0  24 12 |  0  8  4   0  0 12 |  *  * 5  *
sefa( β3β3β3o ) ♦  4 |  2  1   2  1 |  0  0  0   2  1  1 |  *  * * 60

starting figure: x3x3x3o