In geometry

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 great complex icosidodecahedron is a degenerate uniform star polyhedron. It has 12 vertices, and 60 (doubled) edges, and 32 faces, 12 pentagram

Pentagram

A pentagram is the shape of a five-pointed star drawn with five straight strokes...

s and 20 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. 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

The great complex icosidodecahedron can be considered a compound of the small stellated dodecahedron, {5/2,5}, and great icosahedron, {3,5/2}, sharing the same vertices and edges, while the second is hidden, being completely contained inside the first.

Its two-dimensional analogue would be the compound of a regular 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...

, {5}, and regular pentagram

Pentagram

A pentagram is the shape of a five-pointed star drawn with five straight strokes...

, {5/2}.

Compound polyhedron Small stellated dodecahedron Great icosahedron Compound Compound polygon 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... Pentagram Pentagram A pentagram is the shape of a five-pointed star drawn with five straight strokes... Compound

See also

• Small complex icosidodecahedron
  Small complex icosidodecahedron
  In geometry, the small complex icosidodecahedron is a degenerate uniform star polyhedron. It has 32 faces , 60 edges and 12 vertices...
  
  
• Small complex rhombicosidodecahedron
  Small complex rhombicosidodecahedron
  In 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