Acronym	hossidgyt
Name	hollow small-stellated-dodecahedral gyrotrigonism
Circumradius	sqrt[(11+sqrt(5))/24] = 0.742632
Face vector	36, 270, 516, 288, 39
Grünbaumian relatives: hossidgyt + 3 2sissid   general polytopal classes: scaliform
External links

Incidence matrix according to Dynkin symbol

reduced( xoo5/2oxo5/2oox5/2*a&#x by x5/2o5/2o5/2*a each )   → 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 |  5  10 |  5  30  10 | 10 12  20 | 2 11
-------------------------------------+----+--------+------------+-----------+-----
reduced( x..   ...   ...         ) & |  2 | 90   * |  2   4   0 |  4  4   2 | 2  4
         oo.5/2oo.5/2oo.5/2*a&#x   & |  2 |  * 180 |  0   4   2 |  2  2   5 | 1  4
-------------------------------------+----+--------+------------+-----------+-----
reduced( x..5/2o..   ...         ) & |  5 |  5   0 | 36   *   * |  2  2   0 | 2  2 {5/2}
         xo.   ...   ...     &#x   & |  3 |  1   2 |  * 360   * |  1  1   1 | 1  2
         ooo5/2ooo5/2ooo5/2*a&#x     |  3 |  0   3 |  *   * 120 |  0  0   3 | 0  3
-------------------------------------+----+--------+------------+-----------+-----
         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
-------------------------------------+----+--------+------------+-----------+-----
reduced( xo.5/2ox.5/2oo.5/2*a&#x ) & ♦ 24 | 60  60 | 24 120   0 | 12 24   0 | 3  *
         xoo5/2oxo   ...     &#x   & ♦ 11 | 10  20 |  2  20  10 |  1  2  10 | * 36