Small complex icosidodecahedron

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.

Small complex icosidodecahedron
TypeUniform star polyhedron
ElementsF = 32, E = 60 (30x2)
V = 12 (χ = −16)
Faces by sides20{3}+12{5}
Wythoff symbol3/2 5
Symmetry groupIh, [5,3], *532
Index referencesU-, C-, W-
Dual polyhedronSmall complex icosidodecacron
Vertex figure
(3/2.5)5
(3.5)5/3
Bowers acronymCid

A small complex icosidodecahedron can be constructed from a number of different vertex figures.

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
Icosahedron Great dodecahedron Compound

See also

References

  • Coxeter, Harold Scott MacDonald; Longuet-Higgins, M. S.; Miller, J. C. P. (1954), "Uniform polyhedra", Philosophical Transactions of the Royal Society of London. Series A. Mathematical and Physical Sciences, 246 (916): 401–450, doi:10.1098/rsta.1954.0003, ISSN 0080-4614, JSTOR 91532, MR 0062446, S2CID 202575183 (Table 6, degenerate cases)
  • Weisstein, Eric W. "Small complex icosidodecahedron". MathWorld.
  • Klitzing, Richard. "3D uniform polyhedra x3/2o5o5*a - cid".
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.