In general, an icosidodecahedron is a 32-faced polyhedron .

"The"
(regular) icosidodecahedron is the 32-faced Archimedean
solid
with faces .
It is one of the two convex quasiregular polyhedra .
It is also uniform polyhedron and Wenninger model . It has Schläfli
symbol
and Wythoff symbol .

It is implemented in the Wolfram Language
as PolyhedronData ["Icosidodecahedron" ].

Several symmetric projections of the icosidodecahedron are illustrated above. The dual polyhedron is the rhombic
triacontahedron . The polyhedron vertices
of an icosidodecahedron of polyhedron edge length
are ,
,
,
,
,
.
The 30 polyhedron vertices of an octahedron
5-compound form an icosidodecahedron (Ball and Coxeter 1987). Faceted
versions include the small icosihemidodecahedron
and small dodecahemidodecahedron .

The icosidodecahedron constructed in origami is illustrated above (Kasahara and Takahama 1987, pp. 48-49). This construction uses 120 sonobè
units, each made from a single sheet of origami paper.

The faces of the icosidodecahedron consist of 20 triangles and 12 pentagons. Furthermore, its 60 edges are bisected perpendicularly by those of the reciprocal rhombic
triacontahedron (Ball and Coxeter 1987).

Five octahedra of edge length can be inscribed on the vertices of an icosidodecahedron
of unit edge length, resulting in the beautiful octahedron
5-compound .

The inradius of the dual, midradius of the solid and dual, and circumradius of the solid for are

The surface area and volume
for an icosidodecahedron are given by

The distance to the centers of the triangular and pentagonal faces are

The dihedral angle between triangular and pentagonal
faces is

See also Archimedean Solid ,

Equilateral Zonohedron ,

Great Icosidodecahedron ,

Icosidodecahedral Graph ,

Quasiregular
Polyhedron ,

Small Icosihemidodecahedron ,

Small Dodecahemidodecahedron
Explore with Wolfram|Alpha
References Ball, W. W. R. and Coxeter, H. S. M. Mathematical
Recreations and Essays, 13th ed. New York: Dover, p. 137, 1987. Cundy,
H. and Rollett, A. "Icosidodecahedron. ." §3.7.8 in Mathematical
Models, 3rd ed. Stradbroke, England: Tarquin Pub., p. 108, 1989. Kasahara,
K. "From Regular to Semiregular Polyhedrons." Origami
Omnibus: Paper-Folding for Everyone. Tokyo: Japan Publications, pp. 220-221,
1988. Kasahara, K. and Takahama, T. Origami
for the Connoisseur. Tokyo: Japan Publications, 1987. Geometry
Technologies. "Icosidodecahedron." http://www.scienceu.com/geometry/facts/solids/icosidodeca.html . Wenninger,
M. J. "The Icosidodecahedron." Model 12 in Polyhedron
Models. Cambridge, England: Cambridge University Press, pp. 26 and 73,
1989.
Cite this as:
Weisstein, Eric W. "Icosidodecahedron."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/Icosidodecahedron.html

Subject classifications More... Less...