Acronym	grid
TOCID symbol	tID
Name	great (convex) rhombicosidodecahedron (i.e. not qrid), truncated icosidodecahedron, omnitruncated icosahedron, omnitruncated dodecahedron
	© ©
Circumradius	sqrt[31+12 sqrt(5)]/2 = 3.802395
Vertex figure	[4,6,10]
Vertex layers	Layer Symmetry Subsymmetries   o3o5o o3o . o . o . o5o 1 x3x5x x3x . {6} first x . x {4} first . x5x {10} first 2 x3F . u . F . u5x 3 u3U . x . C . x5F 4a x3A . X . U . x5U 4b X3F . 5 B3x . F . A . u5F 6 F3C . B . F . X5x 7 D3x . Y . x . x5X 8 U3C . U . D . F5u 9 D3F . D . X . U5x 10a F3D . H . u . F5x 10b A . B 11 C3U . F . H . x5u 12a x3D . J . x . x5x opposite {10} 12b C . Y 12c x . J 13a C3F . J . x   13b C . Y 13c x . J 14 x3B . F . H 15a A3x . H . u 15b F3X . A . B 16 U3u . D . X 17 F3x . U . D 18 x3x . opposite {6} Y . x 19   B . F 20 F . A 21 X . U 22 x . C 23 u . F 24 x . x opposite {4} (F=x+f, U=2f, X=2x+f, A=3f, B=2x+2f, C=x+2f, D=x+3f, Y=3x+2f, H=2x+3f, J=4f)
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex – no other uniform polyhedral members)
Dihedral angles	between {4} and {6}:   arccos(-(1+sqrt(5))/sqrt(12)) = 159.094843° between {4} and {10}:   arccos(-sqrt[(5+sqrt(5))/10]) = 148.282526° between {6} and {10}:   arccos(-sqrt[(5+2 sqrt(5))/15]) = 142.622632°
Face vector	120, 180, 62
Confer	variations: a3b5c   f3x5x   v3x5f   f3v5v   x3(-x)5f   general polytopal classes: Wythoffian polyhedra
External links

As abstract polytope grid is isomorphic to gaquatid, thereby replacing decagons by decagrams.

When looking more into classes of isogonal variants, then this polyhedron also could be addressed as a truncated icosidodecahedron. However true truncation would not produce squares there. In fact it rather would produce x3t5f instead, where the relative size of t depends on the truncational depth in an inverse ratio.

Incidence matrix according to Dynkin symbol

x3x5x

. . . | 120 |  1  1  1 |  1  1  1
------+-----+----------+---------
x . . |   2 | 60  *  * |  1  1  0
. x . |   2 |  * 60  * |  1  0  1
. . x |   2 |  *  * 60 |  0  1  1
------+-----+----------+---------
x3x . |   6 |  3  3  0 | 20  *  *
x . x |   4 |  2  0  2 |  * 30  *
. x5x |  10 |  0  5  5 |  *  * 12

snubbed forms: β3x5x, x3β5x, x3x5β, β3β5x, β3x5β, x3β5β, s3s5s, β3β5β