Acronym ... Name β3x3x5β (?) Circumradius ...

No uniform realisation is possible.

Incidence matrix according to Dynkin symbol

β3x3x5β

both( . . . . ) | 14400 |    1    1    1    1    1 |    1    1    1    1    2    2    1 |   1    1   1   1    2
----------------+-------+--------------------------+------------------------------------+----------------------
both( . x . . ) |     2 | 7200    *    *    *    * |    1    1    0    0    1    0    1 |   1    1   0   1    1
both( . . x . ) |     2 |    * 7200    *    *    * |    1    0    1    1    0    1    0 |   1    0   1   1    1
both( s .2. s ) |     2 |    *    * 7200    *    * |    0    0    0    0    2    2    0 |   0    1   1   0    2
sefa( β3x . . ) |     2 |    *    *    * 7200    * |    0    1    0    1    1    0    0 |   1    1   0   0    1
sefa( . . x5β ) |     2 |    *    *    *    * 7200 |    0    0    1    0    0    1    1 |   0    0   1   1    1
----------------+-------+--------------------------+------------------------------------+----------------------
both( . x3x . ) |     6 |    3    3    0    0    0 | 2400    *    *    *    *    *    * |   1    0   0   1    0
β3x . .        6 |    3    0    0    3    0 |    * 2400    *    *    *    *    * |   1    1   0   0    0
. . x5β       10 |    0    5    0    0    5 |    *    * 1440    *    *    *    * |   0    0   1   1    0
sefa( β3x3x . ) |     6 |    0    3    0    3    0 |    *    *    * 2400    *    *    * |   1    0   0   0    1
sefa( β3x 2 β ) |     4 |    1    0    2    1    0 |    *    *    *    * 7200    *    * |   0    1   0   0    1
sefa( β 2 x5β ) |     4 |    0    1    2    0    1 |    *    *    *    *    * 7200    * |   0    0   1   0    1
sefa( . x3x5β ) |     6 |    3    0    0    0    3 |    *    *    *    *    *    * 2400 |   0    0   0   1    1
----------------+-------+--------------------------+------------------------------------+----------------------
β3x3x .       24 |   12   12    0   12    0 |    4    4    0    4    0    0    0 | 600    *   *   *    *
β3x 2 β       12 |    6    0    6    6    0 |    0    2    0    0    6    0    0 |   * 1200   *   *    *
β 2 x5β       20 |    0   10   10    0   10 |    0    0    2    0    0   10    0 |   *    * 720   *    *
. x3x5β      120 |   60   60    0    0   60 |   20    0   12    0    0    0   20 |   *    *   * 120    *
sefa( β3x3x5β )     12 |    3    3    6    3    3 |    0    0    0    1    3    3    1 |   *    *   *   * 2400

starting figure: x3x3x5x