Acronym	tagyrid, J74
Name	trigyrated rhombicosidodecahedron
	© ©
Circumradius	sqrt[sqrt(5)+11/4] = 2.232951
Vertex figures	[3,4,4,5], [3,4,5,4]
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°
Face vector	60, 120, 62
Confer	uniform relative: srid   related Johnson solids: pecu   tedrid   general polytopal classes: Johnson solids
External links

Incidence matrix

3 * * * * * * * * * * * | 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
* 6 * * * * * * * * * * | 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 
* * 6 * * * * * * * * * | 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 
* * * 6 * * * * * * * * | 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 gc 
* * * * 6 * * * * * * * | 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 
* * * * * 6 * * * * * * | 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 0 0 gc 
* * * * * * 3 * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 1 0 0 2 1 0 0 0 0 0 gc 
* * * * * * * 6 * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 
* * * * * * * * 6 * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 
* * * * * * * * * 3 * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 2 0 0 0 | 0 0 0 0 0 0 0 0 1 0 0 0 2 0 1 0 0 
* * * * * * * * * * 6 * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 | 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 
* * * * * * * * * * * 3 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 2 1 
------------------------+-------------------------------------------------+----------------------------------
2 0 0 0 0 0 0 0 0 0 0 0 | 3 * * * * * * * * * * * * * * * * * * * * * * * | 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 0 0 0 0 0 0 0 0 | * 6 * * * * * * * * * * * * * * * * * * * * * * | 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 2 0 0 0 0 0 0 0 0 0 0 | * * 3 * * * * * * * * * * * * * * * * * * * * * | 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 0 0 0 0 0 0 0 0 0 | * * * 6 * * * * * * * * * * * * * * * * * * * * | 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 1 0 0 0 0 0 0 0 0 | * * * * 6 * * * * * * * * * * * * * * * * * * * | 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 gc
0 0 2 0 0 0 0 0 0 0 0 0 | * * * * * 3 * * * * * * * * * * * * * * * * * * | 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 1 1 0 0 0 0 0 0 0 0 | * * * * * * 6 * * * * * * * * * * * * * * * * * | 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 gc
0 0 1 0 1 0 0 0 0 0 0 0 | * * * * * * * 6 * * * * * * * * * * * * * * * * | 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0
0 0 0 2 0 0 0 0 0 0 0 0 | * * * * * * * * 3 * * * * * * * * * * * * * * * | 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 gc
0 0 0 1 0 1 0 0 0 0 0 0 | * * * * * * * * * 6 * * * * * * * * * * * * * * | 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 gc
0 0 0 0 2 0 0 0 0 0 0 0 | * * * * * * * * * * 3 * * * * * * * * * * * * * | 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 1 1 0 0 0 0 0 0 | * * * * * * * * * * * 6 * * * * * * * * * * * * | 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 gc
0 0 0 0 1 0 0 1 0 0 0 0 | * * * * * * * * * * * * 6 * * * * * * * * * * * | 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0
0 0 0 0 0 1 1 0 0 0 0 0 | * * * * * * * * * * * * * 6 * * * * * * * * * * | 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 gc
0 0 0 0 0 1 0 1 0 0 0 0 | * * * * * * * * * * * * * * 6 * * * * * * * * * | 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 gc
0 0 0 0 0 0 1 0 1 0 0 0 | * * * * * * * * * * * * * * * 6 * * * * * * * * | 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 gc
0 0 0 0 0 0 0 1 1 0 0 0 | * * * * * * * * * * * * * * * * 6 * * * * * * * | 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0
0 0 0 0 0 0 0 1 0 1 0 0 | * * * * * * * * * * * * * * * * * 6 * * * * * * | 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0
0 0 0 0 0 0 0 0 2 0 0 0 | * * * * * * * * * * * * * * * * * * 3 * * * * * | 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0
0 0 0 0 0 0 0 0 1 0 1 0 | * * * * * * * * * * * * * * * * * * * 6 * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0
0 0 0 0 0 0 0 0 0 1 1 0 | * * * * * * * * * * * * * * * * * * * * 6 * * * | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0
0 0 0 0 0 0 0 0 0 0 2 0 | * * * * * * * * * * * * * * * * * * * * * 3 * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0
0 0 0 0 0 0 0 0 0 0 1 1 | * * * * * * * * * * * * * * * * * * * * * * 6 * | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0
0 0 0 0 0 0 0 0 0 0 0 2 | * * * * * * * * * * * * * * * * * * * * * * * 3 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1
------------------------+-------------------------------------------------+----------------------------------
3 0 0 0 0 0 0 0 0 0 0 0 | 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * * * *
2 2 0 0 0 0 0 0 0 0 0 0 | 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * 3 * * * * * * * * * * * * * * *
1 2 2 0 0 0 0 0 0 0 0 0 | 0 2 0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * 3 * * * * * * * * * * * * * *
0 2 0 2 0 0 0 0 0 0 0 0 | 0 0 1 0 2 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * 3 * * * * * * * * * * * * * gc
0 1 1 1 0 0 0 0 0 0 0 0 | 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * 6 * * * * * * * * * * * * gc
0 0 2 0 2 0 0 0 0 0 0 0 | 0 0 0 0 0 1 0 2 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * 3 * * * * * * * * * * *
0 0 1 1 1 1 0 0 0 0 0 0 | 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * 6 * * * * * * * * * * gc
0 0 0 2 0 2 1 0 0 0 0 0 | 0 0 0 0 0 0 0 0 1 2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 | * * * * * * * 3 * * * * * * * * * gc
0 0 0 0 2 0 0 2 0 1 0 0 | 0 0 0 0 0 0 0 0 0 0 1 0 2 0 0 0 0 2 0 0 0 0 0 0 | * * * * * * * * 3 * * * * * * * *
0 0 0 0 1 1 0 1 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 | * * * * * * * * * 6 * * * * * * * gc
0 0 0 0 0 1 1 1 1 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 | * * * * * * * * * * 6 * * * * * * gc
0 0 0 0 0 0 1 0 2 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 1 0 0 0 0 0 | * * * * * * * * * * * 3 * * * * * gc
0 0 0 0 0 0 0 1 1 1 1 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 | * * * * * * * * * * * * 6 * * * *
0 0 0 0 0 0 0 0 2 0 2 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 0 2 0 | * * * * * * * * * * * * * 3 * * *
0 0 0 0 0 0 0 0 0 1 2 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 | * * * * * * * * * * * * * * 3 * *
0 0 0 0 0 0 0 0 0 0 2 2 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 | * * * * * * * * * * * * * * * 3 *
0 0 0 0 0 0 0 0 0 0 0 3 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 | * * * * * * * * * * * * * * * * 1

gc = belongs to gyrocap