Either base of this Grünbaumian polyteron happens to be 3rasishi. Accordingly their vertices, edges and pentagrams are coincident by 3, the pentagons are coincident with the {10/2}, resp. the dids are coincident with the 2dids. And even the 3does look localy like 3-covers as well.

Incidence matrix according to Dynkin symbol

β2β5o5/2x5o

both( . . .   . . ) | 7200 |     4    2    2 |    2    2    4    1    3    4 |   1   1    2   2    6   2 |   2 1   3
--------------------+------+-----------------+-------------------------------+---------------------------+----------
both( . . .   x . ) |    2 | 14400    *    * |    1    1    1    0    0    1 |   1   0    1   1    2   1 |   1 1   2
      β2β .   . .   |    2 |     * 7200    * |    0    0    2    0    2    0 |   0   1    1   0    4   0 |   2 0   2
sefa( . β5o   . . ) |    2 |     *    * 7200 |    0    0    0    1    1    2 |   0   1    0   2    2   1 |   2 1   1
--------------------+------+-----------------+-------------------------------+---------------------------+----------
both( . . o5/2x . ) |    5 |     5    0    0 | 2880    *    *    *    *    * |   1   0    0   1    1   0 |   1 1   1
both( . . .   x5o ) |    5 |     5    0    0 |    * 2880    *    *    *    * |   1   0    1   0    0   1 |   0 1   2
      β2β 2   x .   |    4 |     2    2    0 |    *    * 7200    *    *    * |   0   0    1   0    2   0 |   1 0   2
      . β5o   . .   |    5 |     0    0    5 |    *    *    * 1440    *    * |   0   1    0   2    0   0 |   2 1   0  {5/2}
sefa( β2β5o   . . ) |    3 |     0    2    1 |    *    *    *    * 7200    * |   0   1    0   0    2   0 |   2 0   1
sefa( . β5o5/2x . ) |   10 |     5    0    5 |    *    *    *    *    * 2880 |   0   0    0   1    1   1 |   1 1   1  {10/2}
--------------------+------+-----------------+-------------------------------+---------------------------+----------
both( . . o5/2x5o ) ♦   30 |    60    0    0 |   12   12    0    0    0    0 | 240   *    *   *    *   * |   0 1   1
      β2β5o   . .   ♦   10 |     0   10   10 |    0    0    0    2   10    0 |   * 720    *   *    *   * |   2 0   0
      β2β 2   x5o   ♦   10 |    10    5    0 |    0    2    5    0    0    0 |   *   * 1440   *    *   * |   0 0   2
      . β5o5/2x .   ♦   60 |    60    0   60 |   12    0    0   12    0   12 |   *   *    * 240    *   * |   1 1   0
sefa( β2β5o5/2x . ) ♦   15 |    10   10    5 |    1    0    5    0    5    1 |   *   *    *   * 2880   * |   1 0   1
sefa( . β5o5/2x5o ) ♦   60 |    60    0   30 |    0   12    0    0    0   12 |   *   *    *   *    * 240 |   0 1   1
--------------------+------+-----------------+-------------------------------+---------------------------+----------
      β2β5o5/2x .   ♦  120 |   120  120  120 |   24    0   60   24  120   24 |   0  12    0   2   24   0 | 120 *   *
      . β5o5/2x5o   ♦ 3600 |  7200    0 3600 | 1440 1440    0  720    0 1440 | 120   0    0 120    0 120 |   * 2   *
sefa( β2β5o5/2x5o ) ♦   90 |   120   60   30 |   12   24   60    0   30   12 |   1   0   12   0   12   1 |   * * 240

starting figure: x x5o5/2x5o

oo5xx5/2xo5/2ox5/2*b&#x   → height = sqrt[(sqrt(5)-1)/2] = 0.786151

o.5o.5/2o.5/2o.5/2*b    & | 7200 |     4    2    2 |    2    4    2    1    4    3 |   2   1   2    2    6   1 | 1   3   2
--------------------------+------+-----------------+-------------------------------+---------------------------+----------
.. x.   ..   ..         & |    2 | 14400    *    * |    1    1    1    0    1    0 |   1   1   1    1    2   0 | 1   2   1
.. ..   x.   ..         & |    2 |     * 7200    * |    0    2    0    1    0    1 |   1   0   2    0    2   1 | 1   1   2
oo5oo5/2oo5/2oo5/2*b&#x   |    2 |     *    * 7200 |    0    0    0    0    2    2 |   0   0   0    1    4   1 | 0   2   2
--------------------------+------+-----------------+-------------------------------+---------------------------+----------
o.5x.   ..   ..         & |    5 |     5    0    0 | 2880    *    *    *    *    * |   1   1   0    1    0   0 | 1   2   0
.. x.5/2x.   ..         & |   10 |     5    5    0 |    * 2880    *    *    *    * |   1   0   1    0    1   0 | 1   1   1
.. x.   ..   o.5/2*b    & |    5 |     5    0    0 |    *    * 2880    *    *    * |   0   1   1    0    1   0 | 1   1   1
.. ..   x.5/2o.         & |    5 |     0    5    0 |    *    *    * 1440    *    * |   0   0   2    0    0   1 | 1   0   2
.. xx   ..   ..     &#x   |    4 |     2    0    2 |    *    *    *    * 7200    * |   0   0   0    1    2   0 | 0   2   1
.. ..   xo   ..     &#x & |    3 |     0    1    2 |    *    *    *    *    * 7200 |   0   0   0    0    2   1 | 0   1   2
--------------------------+------+-----------------+-------------------------------+---------------------------+----------
o.5x.5/2x.   ..         & ♦   60 |    60   30    0 |   12   12    0    0    0    0 | 240   *   *    *    *   * | 1   1   0
o.5x.   ..   o.5/2*b    & ♦   30 |    60    0    0 |   12    0   12    0    0    0 |   * 240   *    *    *   * | 1   1   0
.. x.5/2x.5/2o.5/2*b    & ♦   60 |    60   60    0 |    0   12   12   12    0    0 |   *   * 240    *    *   * | 1   0   1
oo5xx   ..   ..     &#x   ♦   10 |    10    0    5 |    2    0    0    0    5    0 |   *   *   * 1440    *   * | 0   2   0
.. xx5/2xo   ..     &#x & ♦   15 |    10    5   10 |    0    1    1    0    5    5 |   *   *   *    * 2880   * | 0   1   1
.. ..   xo5/2ox     &#x   ♦   10 |     0   10   10 |    0    0    0    2    0   10 |   *   *   *    *    * 720 | 0   0   2
--------------------------+------+-----------------+-------------------------------+---------------------------+----------
o.5x.5/2x.5/2o.5/2*b    & ♦ 3600 |  7200 3600    0 | 1440 1440 1440  720    0    0 | 120 120 120    0    0   0 | 2   *   *
oo5xx5/2xo   ..     &#x & ♦   90 |   120   30   60 |   24   12   12    0   60   30 |   1   1   0   12   12   0 | * 240   *
.. xx5/2xo5/2ox5/2*b&#x   ♦  120 |   120  120  120 |    0   24   24   24   60  120 |   0   0   2    0   24  12 | *   * 120