Acronym	gadsid
Name	great disnub dodecahedron, compound of 12 pap
	©
Circumradius	sqrt[(5+sqrt(5))/8] = 0.951057
Vertex figure	[33,5]
Dihedral angles (at margins)	between {3} and {3}:   arccos(-sqrt(5)/3) = 138.189685° between {3} and {5}:   arccos(-sqrt[(5-2 sqrt(5))/15]) = 100.812317°
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Pentagon planes coincide by pairs. So faces either can be considered separately (type A), or are considered as (general) 2-pentagon-compounds (type B).

Further, instead of considering individual pap, it can likewise be seen as a compound of 6 (general) 2-pap-compounds (type C).

This compound has rotational freedom. At φ = 0° all pap coincide pairwise in a double cover of gassid, else each pap pair rotate in different direction araoud their common axis. For φ = 36° all the 12 pap will be vertex inscribed into an ike.

Incidence matrix

(Type A)

 120 |   2   2 |   3  1 ||  1
-----+---------+--------++---
   2 | 120   * |   1  1 ||  1
   2 |   * 120 |   2  0 ||  1
-----+---------+--------++---
   3 |   1   2 | 120  * ||  1
   5 |   5   0 |   * 24 ||  1
-----+---------+--------++---
♦ 10 |  10  10 |  10  2 || 12

(Type B)

 120 |   2   2 |   3  1 ||  1
-----+---------+--------++---
   2 | 120   * |   1  1 ||  1
   2 |   * 120 |   2  0 ||  1
-----+---------+--------++---
   3 |   1   2 | 120  * ||  1
  10 |  10   0 |   * 12 ||  2
-----+---------+--------++---
♦ 10 |  10  10 |  10  2 || 12

(Type C)

120 |   2   2 |   3  1 || 1
----+---------+--------++--
  2 | 120   * |   1  1 || 1
  2 |   * 120 |   2  0 || 1
----+---------+--------++--
  3 |   1   2 | 120  * || 1
  5 |   5   0 |   * 24 || 1
----+---------+--------++--
 20 |  20  20 |  20  4 || 6  (2-pap-compounds with rotational freedom)