No uniform realisation is possible.

Incidence matrix according to Dynkin symbol

β3β3o3β

both( . . . . ) | 60 |  2  2   4  2  2 |  2  1  1  3   6  3  4 | 1  2  1 1  5
----------------+----+-----------------+-----------------------+-------------
both( s . 2 s ) |  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( . β3o . ) |  2 |  *  *   * 60  * |  0  1  0  1   0  0  1 | 1  0  0 1  1
sefa( . . o3β ) |  2 |  *  *   *  * 60 |  0  0  1  0   0  1  1 | 0  0  1 1  1
----------------+----+-----------------+-----------------------+-------------
both( s3s . . ) ♦  3 |  0  0   3  0  0 | 40  *  *  *   *  *  * | 1  1  0 0  0
      . β3o .   ♦  3 |  0  0   0  3  0 |  * 20  *  *   *  *  * | 1  0  0 1  0
      . . o3β   ♦  3 |  0  0   0  0  3 |  *  * 20  *   *  *  * | 0  0  1 1  0
sefa( β3β3o . ) |  3 |  0  0   2  1  0 |  *  *  * 60   *  *  * | 1  0  0 0  1
sefa( s3s 2 s ) |  3 |  1  1   1  0  0 |  *  *  *  * 120  *  * | 0  1  0 0  1
sefa( β 2 o3β ) |  3 |  2  0   0  0  1 |  *  *  *  *   * 60  * | 0  0  1 0  1
sefa( . β3o3β ) |  4 |  0  2   0  1  1 |  *  *  *  *   *  * 60 | 0  0  0 1  1
----------------+----+-----------------+-----------------------+-------------
      β3β3o .   ♦ 12 |  0  0  24 12  0 |  8  4  0 12   0  0  0 | 5  *  * *  *
both( s3s 2 s ) ♦  6 |  3  3   6  0  0 |  2  0  0  0   6  0  0 | * 20  * *  *
      β 2 o3β   ♦  6 |  6  0   0  0  6 |  0  0  2  0   0  6  0 | *  * 10 *  *
      . β3o3β   ♦ 12 |  0 12   0 12 12 |  0  4  4  0   0  0 12 | *  *  * 5  *
sefa( β3β3o3β ) ♦  5 |  2  2   2  1  1 |  0  0  0  1   2  1  1 | *  *  * * 60

starting figure: x3x3o3x