In
geometry, the great complex icosidodecahedron is a degenerate
uniform star polyhedron
In geometry, a uniform star polyhedron is a self-intersecting uniform polyhedron. They are also sometimes called nonconvex polyhedra to imply self-intersecting. Each polyhedron can contain either star polygon faces, star polygon vertex figures, ...
. It has 12 vertices, and 60 (doubled) edges, and 32 faces, 12
pentagrams and 20
triangles. 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 figures.
As a compound
The great complex icosidodecahedron can be considered a
compound of the
small stellated dodecahedron, , and
great icosahedron, , sharing the same vertices and edges, while the second is hidden, being completely contained inside the first.
{,
,
{, class=wikitable width=300
, + Compound polyhedron
,

,

,

, - align=center
,
Small stellated dodecahedron
,
Great icosahedron
, Compound
See also
*
Small complex icosidodecahedron
*
Small complex rhombicosidodecahedron
*
Complex rhombidodecadodecahedron
*
Great complex rhombicosidodecahedron
References
* (Table 6, degenerate cases)
*
* {{KlitzingPolytopes, polyhedra-neu.htm, 3D uniform polyhedra, o5/3x3o5*a and o3/2x5/2o5*a - gacid
Polyhedra
Polyhedral compounds