This gyrotrigonism uses the Grünbaumian cells 2sissid for the corners of that lace city trigon and therefore becomes such itself. However these double covers might be reduced, then leading to hossidgyt.

Incidence matrix according to Dynkin symbol

xoo5/2oxo5/2oox5/2*a&#x   → height (1,2) = h(1,3) = height(2,3) = sqrt[(sqrt(5)-1)/2] = 0.786151

o..5/2o..5/2o..5/2*a    & | 36 |  10  10 | 10  30  10 | 1 10 12  20 | 2 11
--------------------------+----+---------+------------+-------------+-----
x..   ...   ...         & |  2 | 180   * |  2   2   0 | 1  2  2   1 | 2  2
oo.5/2oo.5/2oo.5/2*a&#x & |  2 |   * 180 |  0   4   2 | 0  2  2   5 | 1  4
--------------------------+----+---------+------------+-------------+-----
x..5/2o..   ...         & |  5 |   5   0 | 72   *   * | 1  1  1   0 | 2  1 {5/2}
xo.   ...   ...     &#x & |  3 |   1   2 |  * 360   * | 0  1  1   1 | 1  2
ooo5/2ooo5/2ooo5/2*a&#x   |  3 |   0   3 |  *   * 120 | 0  0  0   3 | 0  3
--------------------------+----+---------+------------+-------------+-----
x..5/2o..5/2o..5/2*a    & ♦ 12 |  60   0 | 24   0   0 | 3  *  *   * | 2  0
xo.5/2ox.   ...     &#x & ♦ 10 |  10  10 |  2  10   0 | * 36  *   * | 1  1
...   ox.5/2oo.     &#x & ♦  6 |   5   5 |  1   5   0 | *  * 72   * | 1  1
xoo   ...   ...     &#x & ♦  4 |   1   5 |  0   2   2 | *  *  * 180 | 0  2
--------------------------+----+---------+------------+-------------+-----
xo.5/2ox.5/2oo.5/2*a&#x & ♦ 24 | 120  60 | 48 120   0 | 2 12 24   0 | 3  *
xoo5/2oxo   ...     &#x & ♦ 11 |  10  20 |  2  20  10 | 0  1  2  10 | * 36