In here edges cannot be made the same size. However as a mere alternation, this structure indeed exists. Edge sizes then are |sefa( o5β )| = f = 1.618034 and |sefa( β3β )| = h = 1.732051.

Incidence matrix according to Dynkin symbol

o5β3β5o (N → ∞)

both( . . . . ) | 30N |   2    8   2 |  1   4  1   6   6 | 2 2   4
----------------+-----+--------------+-------------------+--------
sefa( o5β . . ) |   2 | 30N    *   * |  1   0  0   2   0 | 2 0   1  f
sefa( . β3β . ) |   2 |   * 120N   * |  0   1  0   1   1 | 1 1   1  h
sefa( . . β5o ) |   2 |   *    * 30N |  0   0  1   0   2 | 0 2   1  f
----------------+-----+--------------+-------------------+--------
      o5β . .   |   5 |   5    0   0 | 6N   *  *   *   * | 2 0   0  f5/2o
both( . s3s . ) |   3 |   0    3   0 |  * 40N  *   *   * | 1 1   0  pw. coplanar as h3o,o3h-pair (or: ho3oh compound)
      . . β5o   |   5 |   0    0   5 |  *   * 6N   *   * | 0 2   0  f5/2o
sefa( o5β3β . ) |   3 |   1    2   0 |  *   *  * 60N   * | 1 0   1  of&#h
sefa( . β3β5o ) |   3 |   0    2   1 |  *   *  *   * 60N | 0 1   1  of&#h
----------------+-----+--------------+-------------------+--------
      o5β3β .   |  60 |  60  120   0 | 12  40  0  60   0 | N *   *  seside variant
      . β3β5o   |  60 |   0  120  60 |  0  40 12   0  60 | * N   *  seside variant
sefa( o5β3β5o ) |   4 |   1    4   1 |  0   0  0   2   2 | * * 30N  tet variant

or
both( . . . . )   | 15N |   4   8 |  2   4  12 | 4   4
------------------+-----+---------+------------+------
sefa( o5β . . ) & |   2 | 30N   * |  1   0   2 | 2   1  f
sefa( . β3β . )   |   2 |   * 60N |  0   1   2 | 2   1  h
------------------+-----+---------+------------+------
      o5β . .   & |   5 |   5   0 | 6N   *   * | 2   0  f5/2o
both( . s3s . )   |   3 |   0   3 |  * 20N   * | 2   0  pw. coplanar as h3o,o3h-pair (or: ho3oh compound)
sefa( o5β3β . ) & |   3 |   1   2 |  *   * 60N | 1   1  of&#h
------------------+-----+---------+------------+------
      o5β3β .   & |  60 |  60 120 | 12  40  60 | N   *  seside variant
sefa( o5β3β5o )   |   4 |   2   4 |  0   0   4 | * 15N  tet variant

starting figure: o5x3x5o