Note that within 2did not only {10/2} is Grünbaumian, also its vertices, edges, and the 2 types of pentagrams were coincident as well.

Incidence matrix according to Dynkin symbol

xx5/2xo5/2ox5/2*a&#x   → height = sqrt[(sqrt(5)-1)/2] = 0.786151

o.5/2o.5/2o.5/2*a    & | 120 |   2   2   2 |  2  1  1  2   3 | 1  3  1
-----------------------+-----+-------------+-----------------+--------
x.   ..   ..         & |   2 | 120   *   * |  1  1  0  1   0 | 1  2  0
..   x.   ..         & |   2 |   * 120   * |  1  0  1  0   1 | 1  1  1
oo5/2oo5/2oo5/2*a&     |   2 |   *   * 120 |  0  0  0  1   2 | 0  2  1
-----------------------+-----+-------------+-----------------+--------
x.5/2x.   ..         & |  10 |   5   5   0 | 24  *  *  *   * | 1  1  0
x.   ..   o.5/2*a    & |   5 |   5   0   0 |  * 24  *  *   * | 1  1  0
..   x.5/2o.         & |   5 |   0   5   0 |  *  * 24  *   * | 1  0  1
xx   ..   ..     &#x   |   4 |   2   0   2 |  *  *  * 60   * | 0  2  0
..   xo   ..     &#x & |   3 |   0   1   2 |  *  *  *  * 120 | 0  1  1
-----------------------+-----+-------------+-----------------+--------
x.5/2x.5/2o.5/2*a    & ♦  60 |  60  60   0 | 12 12 12  0   0 | 2  *  *
xx5/2xo   ..     &#x & ♦  15 |  10   5  10 |  1  1  0  5   5 | * 24  *
..   xo5/2ox     &#x   ♦  10 |   0  10  10 |  0  0  2  0  10 | *  * 12

β2β5o5/2x

both( . . .   . ) | 120 |   2   2   2 |  1  2  1   3  2 |  1 1  3
------------------+-----+-------------+-----------------+--------
both( . . .   x ) |   2 | 120   *   * |  1  1  0   0  1 |  0 1  2
      β2β .   .   |   2 |   * 120   * |  0  1  0   2  0 |  1 0  2
sefa( . β5o   . ) |   2 |   *   * 120 |  0  0  1   1  1 |  1 1  1
------------------+-----+-------------+-----------------+--------
both( . . o5/2x ) |   5 |   5   0   0 | 24  *  *   *  * |  0 1  1 {5/2}
      β2β .   x   |   4 |   2   2   0 |  * 60  *   *  * |  0 0  2
      . β5o   .   |   5 |   0   0   5 |  *  * 24   *  * |  1 1  0 {5/2}
sefa( β2β5o   . ) |   3 |   0   2   1 |  *  *  * 120  * |  1 0  1
sefa( . β5o5/2x ) |  10 |   5   0   5 |  *  *  *   * 24 |  0 1  1 {10/2}
------------------+-----+-------------+-----------------+--------
      β2β5o   .   ♦  10 |   0  10  10 |  0  0  2  10  0 | 12 *  *
      . β5o5/2x   ♦  60 |  60   0  60 | 12  0 12   0 12 |  * 2  *
sefa( β2β5o5/2x ) ♦  15 |  10  10   5 |  1  5  0   5  1 |  * * 24

starting figure: x x5o5/2x