Acronym	hodidgyt
Name	hollow dodecadodecahedral gyrotrigonism
Circumradius	sqrt[(5+sqrt(5))/6] = 1.098185
Face vector	90, 540, 696, 288, 39
Confer	Grünbaumian relatives: hodidgyt + 3 2did   general polytopal classes: scaliform
External links

Incidence matrix according to Dynkin symbol

reduced( xxo5/2xox5/2oxx5/2*a&#x by x5/2x5/2o5/2*a each )   → height (1,2) = h(1,3) = height(2,3) = sqrt[(sqrt(5)-1)/2] = 0.786151

reduced( o..5/2o..5/2o..5/2*a    ) & | 90 |   4   8 |  2   8  12   4 |  8  4  10 | 2  6
-------------------------------------+----+---------+----------------+-----------+-----
reduced( x..   ...   ...         ) & |  2 | 180   * |  1   2   2   0 |  4  2   2 | 2  3
         oo.5/2oo.5/2oo.5/2*a&#x   & |  2 |   * 360 |  0   1   2   1 |  2  1   3 | 1  3
-------------------------------------+----+---------+----------------+-----------+-----
reduced( x..   ...   o..5/2*a    ) & |  5 |   5   0 | 36   *   *   * |  2  2   0 | 2  2
         xx.   ...   ...     &#x   & |  4 |   2   2 |  * 180   *   * |  2  0   1 | 1  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
-------------------------------------+----+---------+----------------+-----------+-----
reduced( xx.5/2xo.   ...     &#x ) & ♦ 10 |  10  10 |  1   5   5   0 | 72  *   * | 1  1
         ...   xo.5/2ox.     &#x   & ♦ 10 |  10  10 |  2   0  10   0 |  * 36   * | 1  1
         xxo   ...   ...     &#x   & ♦  5 |   2   6 |  0   1   2   2 |  *  * 180 | 0  2
-------------------------------------+----+---------+----------------+-----------+-----
reduced( xx.5/2xo.5/2ox.5/2*a&#x ) & ♦ 60 | 120 120 | 24  60 120   0 | 24 12   0 | 3  *
         xxo5/2xox   ...     &#x   & ♦ 15 |  15  30 |  2  10  20  10 |  2  1  10 | * 36