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

Incidence matrix according to Dynkin symbol

xxo5/2xox5/2oxx5/2*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    & | 180 |   4   4 |  2  2   4   6   2 | 1  6  2   5 | 2  4
--------------------------+-----+---------+-------------------+-------------+-----
x..   ...   ...         & |   2 | 360   * |  1  1   1   1   0 | 1  3  1   1 | 2  2
oo.5/2oo.5/2oo.5/2*a&#x & |   2 |   * 360 |  0  0   1   2   1 | 0  2  1   3 | 1  3
--------------------------+-----+---------+-------------------+-------------+-----
x..5/2x..   ...         & |  10 |  10   0 | 36  *   *   *   * | 1  2  0   0 | 2  1
x..   ...   o..5/2*a    & |   5 |   5   0 |  * 72   *   *   * | 1  1  1   0 | 2  1
xx.   ...   ...     &#x & |   4 |   2   2 |  *  * 180   *   * | 0  2  0   1 | 1  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..5/2x..5/2o..5/2*a    & ♦  60 | 120   0 | 12 24   0   0   0 | 3  *  *   * | 2  0
xx.5/2xo.   ...     &#x & ♦  15 |  15  10 |  1  1   5   5   0 | * 72  *   * | 1  1
...   xo.5/2ox.     &#x & ♦  10 |  10  10 |  0  2   0  10   0 | *  * 36   * | 1  1
xxo   ...   ...     &#x & ♦   5 |   2   6 |  0  0   1   2   2 | *  *  * 180 | 0  2
--------------------------+-----+---------+-------------------+-------------+-----
xx.5/2xo.5/2ox.5/2*a&#x & ♦ 120 | 240 120 | 24 48  60 120   0 | 2 24 12   0 | 3  *
xxo5/2xox   ...     &#x & ♦  20 |  20  30 |  1  2  10  20  10 | 0  2  1  10 | * 36