Acronym	pagydrid, J77
Name	paragyrate diminished rhombicosidodecahedron
VRML	⭳ ©
Circumradius	sqrt[sqrt(5)+11/4] = 2.232951
Vertex figures	[4,5,10], [3,4,5,4], [3,42,5]
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex)
Dihedral angles	between {3} and {4}:   arccos(-(1+sqrt(5))/sqrt(12)) = 159.094843° between {3} and {5}:   arccos(-sqrt[(65-2 sqrt(5))/75]) = 153.942419° between {4} and {4}:   arccos(-2/sqrt(5)) = 153.434949° between {4} and {5}:   arccos(-sqrt[(5+sqrt(5))/10]) = 148.282526° between {4} and {10}:   arccos(-sqrt[(5-sqrt(5))/10]) = 121.717474° between {5} and {10}:   arccos(-1/sqrt(5)) = 116.565051°
Face vector	55, 105, 52
Confer	uniform relative: srid   related Johnson solids: pecu   pabidrid   gyrid   general polytopal classes: Johnson solids
External links

Incidence matrix

10  * * *  *  * * | 1 1  1 0  0  0  0  0 0  0 0 0  0 0 | 1 1 1 0  0 0 0 0 0 0 0  at {10}
 * 10 * *  *  * * | 0 0  1 1  1  1  0  0 0  0 0 0  0 0 | 0 1 1 1  1 0 0 0 0 0 0
 *  * 5 *  *  * * | 0 0  0 0  2  0  2  0 0  0 0 0  0 0 | 0 0 1 0  2 1 0 0 0 0 0
 *  * * 5  *  * * | 0 0  0 0  0  2  0  2 0  0 0 0  0 0 | 0 0 0 1  2 0 1 0 0 0 0
 *  * * * 10  * * | 0 0  0 0  0  0  1  1 1  1 0 0  0 0 | 0 0 0 0  1 1 1 1 0 0 0
 *  * * *  * 10 * | 0 0  0 0  0  0  0  0 0  1 1 1  1 0 | 0 0 0 0  0 0 1 1 1 1 0
 *  * * *  *  * 5 | 0 0  0 0  0  0  0  0 0  0 0 0  2 2 | 0 0 0 0  0 0 0 0 1 2 1  at opposite {5}
------------------+------------------------------------+-----------------------
 2  0 0 0  0  0 0 | 5 *  * *  *  *  *  * *  * * *  * * | 1 1 0 0  0 0 0 0 0 0 0  {4},{10}-join
 2  0 0 0  0  0 0 | * 5  * *  *  *  *  * *  * * *  * * | 1 0 1 0  0 0 0 0 0 0 0  {5},{10}-join
 1  1 0 0  0  0 0 | * * 10 *  *  *  *  * *  * * *  * * | 0 1 1 0  0 0 0 0 0 0 0
 0  2 0 0  0  0 0 | * *  * 5  *  *  *  * *  * * *  * * | 0 1 0 1  0 0 0 0 0 0 0
 0  1 1 0  0  0 0 | * *  * * 10  *  *  * *  * * *  * * | 0 0 1 0  1 0 0 0 0 0 0
 0  1 0 1  0  0 0 | * *  * *  * 10  *  * *  * * *  * * | 0 0 0 1  1 0 0 0 0 0 0
 0  0 1 0  1  0 0 | * *  * *  *  * 10  * *  * * *  * * | 0 0 0 0  1 1 0 0 0 0 0
 0  0 0 1  1  0 0 | * *  * *  *  *  * 10 *  * * *  * * | 0 0 0 0  1 0 1 0 0 0 0
 0  0 0 0  2  0 0 | * *  * *  *  *  *  * 5  * * *  * * | 0 0 0 0  0 1 0 1 0 0 0
 0  0 0 0  1  1 0 | * *  * *  *  *  *  * * 10 * *  * * | 0 0 0 0  0 0 1 1 0 0 0
 0  0 0 0  0  2 0 | * *  * *  *  *  *  * *  * 5 *  * * | 0 0 0 0  0 0 1 0 1 0 0  {3},{5}-join
 0  0 0 0  0  2 0 | * *  * *  *  *  *  * *  * * 5  * * | 0 0 0 0  0 0 0 1 0 1 0  {4},{4}-join
 0  0 0 0  0  1 1 | * *  * *  *  *  *  * *  * * * 10 * | 0 0 0 0  0 0 0 0 1 1 0
 0  0 0 0  0  0 2 | * *  * *  *  *  *  * *  * * *  * 5 | 0 0 0 0  0 0 0 0 0 1 1
------------------+------------------------------------+-----------------------
10  0 0 0  0  0 0 | 5 5  0 0  0  0  0  0 0  0 0 0  0 0 | 1 * * *  * * * * * * *  {10}
 2  2 0 0  0  0 0 | 1 0  2 1  0  0  0  0 0  0 0 0  0 0 | * 5 * *  * * * * * * *
 2  2 1 0  0  0 0 | 0 1  2 0  2  0  0  0 0  0 0 0  0 0 | * * 5 *  * * * * * * *
 0  2 0 1  0  0 0 | 0 0  0 1  0  2  0  0 0  0 0 0  0 0 | * * * 5  * * * * * * *
 0  1 1 1  1  0 0 | 0 0  0 0  1  1  1  1 0  0 0 0  0 0 | * * * * 10 * * * * * *
 0  0 1 0  2  0 0 | 0 0  0 0  0  0  2  0 1  0 0 0  0 0 | * * * *  * 5 * * * * *
 0  0 0 1  2  2 0 | 0 0  0 0  0  0  0  2 0  2 1 0  0 0 | * * * *  * * 5 * * * *
 0  0 0 0  2  2 0 | 0 0  0 0  0  0  0  0 1  2 0 1  0 0 | * * * *  * * * 5 * * *
 0  0 0 0  0  2 1 | 0 0  0 0  0  0  0  0 0  0 1 0  2 0 | * * * *  * * * * 5 * *
 0  0 0 0  0  2 2 | 0 0  0 0  0  0  0  0 0  0 0 1  2 1 | * * * *  * * * * * 5 *
 0  0 0 0  0  0 5 | 0 0  0 0  0  0  0  0 0  0 0 0  0 5 | * * * *  * * * * * * 1  opposite {5}