Great Icosidodecahedron -- from Wolfram MathWorld
- ️Weisstein, Eric W.
The great icosidodecahedron, not to be confused with the great icosahedron or great icosicosidodecahedron,
is the uniform polyhedron with Maeder index
54 (Maeder 1997), Wenninger index 94 (Wenninger 1989), Coxeter index 70 (Coxeter
et al. 1954), and Har'El index 59 (Har'El 1993). It has Schläfli
symbol 
and Wythoff symbol 
. Its faces are 
.
It is a stellated Archimedean solid.
The great icosidodecahedron is implemented in the Wolfram Language as UniformPolyhedron[94],
UniformPolyhedron["GreatIcosidodecahedron"],
UniformPolyhedron[
"Coxeter",
70
],
UniformPolyhedron[
"Kaleido",
59
],
UniformPolyhedron[
"Uniform",
54
],
or UniformPolyhedron[
"Wenninger",
94
].
It is also implemented in the Wolfram
Language as PolyhedronData["GreatIcosidodecahedron"].
Its skeleton is the icosidodecahedral graph.
Its convex hull is a regular icosidodecahedron.
Its circumradius for unit edge length is
where 
is the golden ratio.
Its dual is the great rhombic triacontahedron, with which it is illustrated above.
See also
Explore with Wolfram|Alpha
References
Coxeter, H. S. M.; Longuet-Higgins, M. S.; and Miller, J. C. P. "Uniform Polyhedra." Phil. Trans. Roy.
Soc. London Ser. A 246, 401-450, 1954.Cundy, H. and Rollett,
A. "Great Icosidodecahedron. 
." §3.9.2 in Mathematical
Models, 3rd ed. Stradbroke, England: Tarquin Pub., p. 124, 1989.Har'El,
Z. "Uniform Solution for Uniform Polyhedra." Geometriae Dedicata 47,
57-110, 1993.Maeder, R. E. "54: Great Icosidodecahedron."
1997. https://www.mathconsult.ch/static/unipoly/48.html.Wenninger,
M. J. "Great Icosidodecahedron." Model 94 in Polyhedron
Models. Cambridge, England: Cambridge University Press, p. 147, 1989.
Referenced on Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Great Icosidodecahedron." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GreatIcosidodecahedron.html