Small complex icosidodecahedron
Encyclopedia
In geometry
, the small complex icosidodecahedron is a degenerate uniform star polyhedron. It has 32 faces (20 triangle
s and 12 pentagon
s), 60 (doubled) edges and 12 vertices. All edges are doubled (making it degenerate), sharing 4 faces, but are considered as two overlapping edges as topological polyhedron.
It can be constructed
from a number of different vertex figure
s.
{3,5} and the great dodecahedron {5,5/2} where all vertices and edges coincide. The small complex icosidodecahedron appears to be an icosahedron
because the great dodecahedron is completely contained inside the icosahedron
.
{|
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{| class=wikitable width=300
|+ Compound polyhedron
|
|
|
|- align=center
|Icosahedron
|Great dodecahedron
|Compound
|}
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, the small complex icosidodecahedron is a degenerate uniform star polyhedron. It has 32 faces (20 triangle
Triangle
A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ....
s and 12 pentagon
Pentagon
In geometry, a pentagon is any five-sided polygon. A pentagon may be simple or self-intersecting. The sum of the internal angles in a simple pentagon is 540°. A pentagram is an example of a self-intersecting pentagon.- Regular pentagons :In a regular pentagon, all sides are equal in length and...
s), 60 (doubled) edges and 12 vertices. All edges are doubled (making it degenerate), sharing 4 faces, but are considered as two overlapping edges as topological polyhedron.
It can be constructed
Wythoff construction
In geometry, a Wythoff construction, named after mathematician Willem Abraham Wythoff, is a method for constructing a uniform polyhedron or plane tiling. It is often referred to as Wythoff's kaleidoscopic construction.- Construction process :...
from a number of different vertex figure
Vertex figure
In geometry a vertex figure is, broadly speaking, the figure exposed when a corner of a polyhedron or polytope is sliced off.-Definitions - theme and variations:...
s.
As a compound
It can be seen as a compound of the icosahedronIcosahedron
In geometry, an icosahedron is a regular polyhedron with 20 identical equilateral triangular faces, 30 edges and 12 vertices. It is one of the five Platonic solids....
{3,5} and the great dodecahedron {5,5/2} where all vertices and edges coincide. The small complex icosidodecahedron appears to be an icosahedron
Icosahedron
In geometry, an icosahedron is a regular polyhedron with 20 identical equilateral triangular faces, 30 edges and 12 vertices. It is one of the five Platonic solids....
because the great dodecahedron is completely contained inside the icosahedron
Icosahedron
In geometry, an icosahedron is a regular polyhedron with 20 identical equilateral triangular faces, 30 edges and 12 vertices. It is one of the five Platonic solids....
.
{|
|
{| class=wikitable width=300
|+ Compound polyhedron
|
|
|
|- align=center
|Icosahedron
Icosahedron
In geometry, an icosahedron is a regular polyhedron with 20 identical equilateral triangular faces, 30 edges and 12 vertices. It is one of the five Platonic solids....
|Great dodecahedron
|Compound
|}
See also
- Great complex icosidodecahedronGreat complex icosidodecahedronIn geometry, the great complex icosidodecahedron is a degenerate uniform star polyhedron. It has 12 vertices, and 60 edges, and 32 faces, 12 pentagrams and 20 pentagons...
- Small complex rhombicosidodecahedronSmall complex rhombicosidodecahedronIn geometry, the small complex rhombicosidodecahedron is a degenerate uniform star polyhedron. It has 62 faces , 120 edges and 20 vertices...
- Complex rhombidodecadodecahedron
- Great complex rhombicosidodecahedron