Acronym grid
TOCID symbol tID
Name great (convex) rhombicosidodecahedron (i.e. not qrid),
truncated icosidodecahedron,
omnitruncated icosahedron,
omnitruncated dodecahedron
 
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Circumradius sqrt[31+12 sqrt(5)]/2 = 3.802395
Vertex figure [4,6,10]
Vertex layers
LayerSymmetrySubsymmetries
 o3o5oo3o .o . o. o5o
1x3x5xx3x .
{6} first
x . x
{4} first
. x5x
{10} first
2x3F .u . F. u5x
3u3U .x . C. x5F
4ax3A .X . U. x5U
4bX3F .
5B3x .F . A. u5F
6F3C .B . F. X5x
7D3x .Y . x. x5X
8U3C .U . D. F5u
9D3F .D . X. U5x
10aF3D .H . u. F5x
10bA . B
11C3U .F . H. x5u
12ax3D .J . x. x5x
opposite {10}
12bC . Y
12cx . J
13aC3F .J . x 
13bC . Y
13cx . J
14x3B .F . H
15aA3x .H . u
15bF3X .A . B
16U3u .D . X
17F3x .U . D
18x3x .
opposite {6}
Y . x
19 B . F
20F . A
21X . U
22x . C
23u . F
24x . 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°
Confer
variations:
a3b5c   f3x5x   v3x5f   f3v5v   x3(-x)5f  
External
links
hedrondude   wikipedia   polytopewiki   WikiChoron   mathworld   quickfur

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

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