No uniform realisation is possible.

Incidence matrix according to Dynkin symbol

o3β5o

both( . . . ) | 30 |  4  4 |  2  2  4
--------------+----+-------+---------
sefa( o3β . ) |  2 | 60  * |  1  0  1  x
sefa( . β5o ) |  2 |  * 60 |  0  1  1  f
--------------+----+-------+---------
      o3β .   ♦  3 |  3  0 | 20  *  *
      . β5o   ♦  5 |  0  5 |  * 12  *
sefa( o3β5o ) |  4 |  2  2 |  *  * 30

starting figure: o3x5o

x3o5/3f

. .   . | 30 |  4  4 |  2  4  2
--------+----+-------+---------
x .   . |  2 | 60  * |  1  1  0
. .   f |  2 |  * 60 |  0  1  1
--------+----+-------+---------
x3o   . |  3 |  3  0 | 20  *  *
x .   f |  4 |  2  2 |  * 30  *
. o5/3f |  5 |  0  5 |  *  * 12

x3/2o5/2f

.   .   . | 30 |  4  4 |  2  4  2
----------+----+-------+---------
x   .   . |  2 | 60  * |  1  1  0
.   .   f |  2 |  * 60 |  0  1  1
----------+----+-------+---------
x3/2o   . |  3 |  3  0 | 20  *  *
x   .   f |  4 |  2  2 |  * 30  *
.   o5/2f |  5 |  0  5 |  *  * 12

(-x)3o5/2f

  .  .   . | 30 |  4  4 |  2  4  2
-----------+----+-------+---------
 -x  .   . |  2 | 60  * |  1  1  0
  .  .   f |  2 |  * 60 |  0  1  1
-----------+----+-------+---------
(-x)3o   . |  3 |  3  0 | 20  *  *
(-x) .   f |  4 |  2  2 |  * 30  *
  .  o5/2f |  5 |  0  5 |  *  * 12