Small complex icosidodecahedron
Introduction In geometry, the '''small complex icosidodecahedron''' is a degenerate uniform star polyhedron. Its edges are doubled, making it degenerate. The star has 32 faces (20 triangles and 12 pentagons), 60 (doubled) edges and 12 vertices and 4 sharing faces. The faces in it are considered as two overlapping edges as topological polyhedron.A small complex icosidodecahedron can be constructed from a number of different vertex figures.A very similar figure emerges as a geometrical truncation of the great stellated dodecahedron, where the pentagram faces become doubly-wound pentagons ({5/2} --> {10/2}), making the internal pentagonal planes, and the three meeting at each vertex become triangles, making the external triangular planes.
As a compound The small complex icosidodecahedron can be seen as a compound of the icosahedron {3,5} and the great dodecahedron {5,5/2} where all vertices are precise and edges coincide. The small complex icosidodecahedron resembles an icosahedron, because the great dodecahedron is completely contained inside the icosahedron.+ '''Compound polyhedron'''100px100px101pxIcosahedronGreat dodecahedronCompoundIts two-dimensional analogue would be the compound of a regular pentagon, {5}, representing the icosahedron as the ''n''-dimensional pentagonal polytope, and regular pentagram, {5/2}, as the ''n''-dimensional star. These shapes would share vertices, similarly to how its 3D equivalent shares edges.+ '''Compound polygon'''100px100px100pxPentagonPentagramCompound
See also * Great complex icosidodecahedron* Small complex rhombicosidodecahedron* Complex rhombidodecadodecahedron* Great complex rhombicosidodecahedron
References * (Table 6, degenerate cases)* *