View source for Great inverted snub icosidodecahedron

{{Infobox polytope
|dim = 3
|img=Great inverted snub icosidodecahedron.png
|3d=Great inverted snub icosidodecahedron.stl
|off = Great inverted snub icosidodecahedron.off
|obsa = Gisid
|type=[[Uniform]]
|coxeter = s5/3s3s ({{CDD|node_h|5|rat|3x|node_h|3|node_h|}})
|symmetry = [[Chiral dodecahedral symmetry|H<sub>3</sub>+]], order 60
|army=Non-uniform [[snub dodecahedron|Snid]]
|reg='''Gisid'''
|faces = 20+60 [[triangle]]s, 12 [[pentagram]]s
|edges = 30+60+60
|vertices = 60
|verf = Irregular [[pentagon]], edge lengths 1, 1, 1, 1, ({{radic|5}}–1)/2 <br> {{small|Great inverted snub icosidodecahedron vertfig.png}}
|dual = [[Great inverted pentagonal hexecontahedron]]
|circum =≈ 0.64502
|vol =≈ 2.71387
|density = 13
|euler=2
|dih=3–3: ≈ 89.78760°
|dih2=5/2–3: ≈ 21.61047°
|flags = 600
|pieces = 780
|loc = 65
|conjugate = [[Snub dodecahedron]], [[Great snub icosidodecahedron]], [[Great inverted retrosnub icosidodecahedron]]
|core=Chiral [[order-6 truncated pentakis dodecahedron]]
|conv=No
|orient=Yes
|nat=Tame
}}
{{Distinguish|gissid}}
The '''great inverted snub icosidodecahedron''' or '''gisid''', is a [[uniform]] polyhedron. It consists of 60 snub [[triangle]]s, 20 additional triangles, and 12 [[pentagram]]s. Four triangles and one pentagram meet at each vertex. It can  be constructed by [[alternation]] of the [[great quasitruncated icosidodecahedron]] after setting all edge lengths to be equal.

==Measures==
The circumradius ''R'' ≈ 0.64502 of the great inverted snub icosidodecahedron with unit edge length is the second to smallest positive real root of:
:<math>4096x^{12}-27648x^{10}+47104x^8-35776x^6+13872x^4-2696x^2+209.</math>
Its volume ''V'' ≈ 2.71387 is given by the second to smallest positive real root of:
:<math>\begin{align}&2176782336x^{12}-3195335070720x^{10}+162223191936000x^8+1030526618040000x^6\\
{} &+6152923794150000x^4-182124351550575000x^2+187445810737515625.\end{align}</math>
These same polynomials define the circumradii and volumes of the [[snub dodecahedron]], the [[great snub icosidodecahedron]], and the [[great inverted retrosnub icosidodecahedron]].

==Related polyhedra==
The [[great inverted disnub icosidodecahedron]] is a uniform [[polyhedron compound]] composed of the two opposite chiral forms of the great inverted snub icosidodecahedron.
{{o5/3o3o truncations}}

==External links==
*{{Bowers|snubs|Polyhedron Category 6: Snubs|70}}
*{{Incmats|gisid}}
*{{Wikipedia|Great inverted snub icosidodecahedron}}
*{{Dmccooey|GreatInvertedSnubIcosidodecahedron|Great Inverted Snub icosidodecahedron}}

[[Category:Nonconvex uniform polyhedra]]
[[Category:Snid army]]
[[Category:H3+ symmetry]]
[[Category:Snub polyhedra]]
[[Category:Polyhedra with 92 faces]]