Everything about Icosidodecahedron totally explained
An
icosidodecahedron is a
polyhedron with twenty triangular faces and twelve pentagonal faces. An icosidodecahedron has 30 identical vertices, with two triangles and two pentagons meeting at each, and 60 identical edges, each separating a triangle from a pentagon. As such it's one of the
Archimedean solids and more particularly, a
quasiregular polyhedron.
An icosidodecahedron has icosahedral symmetry, and its first
stellation is the compound of a
dodecahedron and its dual
icosahedron, with the vertices of the icosahedron located at the midpoints of the edges of either. Canonical coordinates for the vertices of an icosidodecahedron with unit edges are the
cyclic permutations of (0,0,±τ), (±1/2, ±τ/2, ±(1+τ)/2), where τ is the
golden ratio, (1+√5)/2. Its
dual polyhedron is the
rhombic triacontahedron. An icosidodecahedron can be split along several planes to form
pentagonal rotundae, which belong among the
Johnson solids.
In the standard nomenclature used for the
Johnson solids, an icosidodecahedron would be called a
pentagonal gyrobirotunda.
Area and volume
The area
A and the volume
V of the icosidodecahedron of edge length
a are:
»
Related polyhedra
The icosidodecahedron is a
rectified dodecahedron and also a rectified
icosahedron, existing as the full-edge truncation between these regular solids.
The Icosidodecahedron contains 12 pentagons of the
dodecahedron and 20 triangles of the
icosahedron:
It is also related to the
Johnson solid called a
pentagonal orthobirotunda created by two
pentagonal rotunda connected as mirror images.
(Dissection) |
Icosidodecahedron
(pentagonal gyrobirotunda) |
Pentagonal orthobirotunda |
Pentagonal rotunda |
|
There are also 9
uniform star polyhedra which share the same
vertex arrangement:
Further Information
Get more info on 'Icosidodecahedron'.
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