Compound of four octahedra

Compound of four octahedra
Type	Uniform compound
Index	UC12
Convex hull	Nonuniform truncated cube
Polyhedra	4 octahedra
Faces	8+24 triangles
Edges	48
Vertices	24
Symmetry group	octahedral (Oh)
Subgroup restricting to one constituent	3-fold antiprismatic (D3d)

This uniform polyhedron compound is a symmetric arrangement of 4 octahedra, considered as triangular antiprisms. It can be constructed by superimposing four identical octahedra, and then rotating each by 60 degrees about a separate axis (that passes through the centres of two opposite octahedral faces).

Cartesian coordinates

Cartesian coordinates for the vertices of this compound are all the permutations of

(±2, ±1, ±2)

References

• Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society 79 (03): 447–457, doi:10.1017/S0305004100052440, MR0397554 .

This polyhedron-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Polyhedral compounds Polyhedron stubs Wikimedia Foundation. 2010. Игры ⚽ Поможем написать реферат Bowman Municipal Airport Asif Bajwa Look at other dictionaries: Compound of four octahedra with rotational freedom — Type Uniform compound Index UC10 Polyhedra 4 octahedra Faces 8+24 triangles …   Wikipedia Compound of eight octahedra with rotational freedom — Type Uniform compound Index UC11 Polyhedra 8 octahedra Faces 16+48 triangles …   Wikipedia Compound of three octahedra — The compound of three octahedra In mathematics, the compound of three octahedra or octahedron 3 compound is a polyhedral compound formed from three regular octahedra, all sharing a common center but rotated with respect to each other. Although… …   Wikipedia Compound of twenty octahedra with rotational freedom — Type Uniform compound Index UC13 Polyhedra 20 octahedra Faces 40+120 triangles …   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 Icosahedral symmetry — A Soccer ball, a common example of a spherical truncated icosahedron, has full icosahedral symmetry. A regular icosahedron has 60 rotational (or orientation preserving) symmetries, and a symmetry order of 120 including transformations that… …   Wikipedia Octahedron — For the album by The Mars Volta, see Octahedron (album). Regular Octahedron (Click here for rotating model) Type Platonic solid Elements F = 8, E = 12 V = 6 (χ = 2) Faces by sides …   Wikipedia Dicopper chloride trihydroxide — IUPAC name Dicopper chloride trihydroxide …   Wikipedia Crystal structure of boron-rich metal borides — Two single crystals of YB66 (1 cm diameter) grown by floating zone technique using (100) oriented seeds. In the top crystal, the seed (left from the black line) has same diameter as the crystal. In the bottom crystal (sliced), the seed is much… …   Wikipedia Keggin structure — is the best known structural form for heteropoly acids. It is the structural form of α–Keggin anions, which have a general formula of [XM12O40] n , where X is the heteroatom (most commonly are P5+, Si4+, or B3+), M is the addenda atom (most… …   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”