Surf Wiki
Save to docs
general/polyhedra

From Surf Wiki (app.surf) — the open knowledge base

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.

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.

IcosahedronGreat dodecahedronCompound

Its 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.

PentagonPentagramCompound

References

  • (Table 6, degenerate cases)
Info: Wikipedia Source

This article was imported from Wikipedia and is available under the Creative Commons Attribution-ShareAlike 4.0 License. Content has been adapted to SurfDoc format. Original contributors can be found on the article history page.

polyhedra polyhedral-compounds
Want to explore this topic further?

Ask Mako anything about Small complex icosidodecahedron — get instant answers, deeper analysis, and related topics.

Research with Mako

Free with your Surf account

Content sourced from Wikipedia, available under CC BY-SA 4.0.

This content may have been generated or modified by AI. CloudSurf Software LLC is not responsible for the accuracy, completeness, or reliability of AI-generated content. Always verify important information from primary sources.

Report