Compound of two great icosahedra

Compound of two great icosahedra
Type	Uniform compound
Index	UC52
Polyhedra	2 great icosahedra
Faces	16+24 triangles
Edges	60
Vertices	24
Symmetry group	octahedral (Oh)
Subgroup restricting to one constituent	pyritohedral (Th)

This uniform polyhedron compound is a composition of 2 great icosahedra, in the same arrangement as in the compound of 2 icosahedra.

The triangles in this compound decompose into two orbits under action of the symmetry group: 16 of the triangles lie in coplanar pairs in octahedral planes, while the other 24 lie in unique planes.

References

• Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society 79: 447–457, doi:10.1017/S0305004100052440, MR0397554 .

External links

• VRML model: [1]

This polyhedron-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Polyhedral compounds Polyhedron stubs Wikimedia Foundation. 2010. Игры ⚽ Нужна курсовая? London Typographical Society Trössing Look at other dictionaries: Compound of five great icosahedra — Type Uniform compound Index UC53 Polyhedra 5 great icosahedra Faces 40+60 …   Wikipedia Compound of two great dodecahedra — Type Uniform compound Index UC48 Polyhedra 2 great dodecahedra Faces 24 penta …   Wikipedia Compound of five tetrahedra — Type Regular compound Index UC5, W24 Elements (As a compound) 5 tetrahedra: F = 20 …   Wikipedia Compound of ten tetrahedra — Type regular compound Index UC6, W25 Elements (As a compound) 10 tetrahedra: F = 40, E = 60, V = 20 …   Wikipedia Polyhedral compound — A polyhedral compound is a polyhedron that is itself composed of several other polyhedra sharing a common centre. They are the three dimensional analogs of polygonal compounds such as the hexagram. Neighbouring vertices of a compound can be… …   Wikipedia List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… …   Wikipedia The fifty nine icosahedra — is a book written and illustrated by H. S. M. Coxeter, P. Du Val, H. T. Flather and J. F. Petrie. It enumerates the stellations of the regular or Platonic icosahedron, according to a set of rules put forward by J. C. P. Miller.The book was… …   Wikipedia Stellation — is a process of constructing new polygons (in two dimensions), new polyhedra in three dimensions, or, in general, new polytopes in n dimensions. The process consists of extending elements such as edges or face planes, usually in a symmetrical way …   Wikipedia chemistry — /kem euh stree/, n., pl. chemistries. 1. the science that deals with the composition and properties of substances and various elementary forms of matter. Cf. element (def. 2). 2. chemical properties, reactions, phenomena, etc.: the chemistry of… …   Universalium Final stellation of the icosahedron — Two symmetric orthographic projections Symmetry group icosahedra …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”