Acronym grid
TOCID symbol tID
Name great rhombicosidodecahedron (but not qrid),
truncated icosidodecahedron
 
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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   WikiChoron   mathworld   quickfur

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


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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