Compound of five truncated cubes

Compound of five truncated cubes
Type	Uniform compound
Index	UC57
Polyhedra	5 truncated cubes
Faces	40 triangles, 30 octagons
Edges	180
Vertices	120
Symmetry group	icosahedral (Ih)
Subgroup restricting to one constituent	pyritohedral (Th)

This uniform polyhedron compound is a composition of 5 truncated cubes, formed by truncating each of the cubes in the compound of 5 cubes.

Cartesian coordinates

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

(±(2+√2), ±√2, ±(2+√2))

(±τ, ±(τ⁻¹+τ⁻¹√2), ±(2τ−1+τ√2))

(±1, ±(τ⁻²−τ⁻¹√2), ±(τ²+τ√2))

(±(1+√2), ±(−τ⁻²−√2), ±(τ²+√2))

(±(τ+τ√2), ±(−τ⁻¹), ±(2τ−1+τ⁻¹√2))

where τ = (1+√5)/2 is the golden ratio (sometimes written φ).

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 Vidas Blekaitis TOE1 Look at other dictionaries: Compound of five uniform great rhombicuboctahedra — Type Uniform compound Index UC67 Polyhedra 5 uniform great rhombicuboctahedra …   Wikipedia Compound of five stellated truncated cubes — Type Uniform compound Index UC58 Polyhedra 5 stellated truncated cubes Faces …   Wikipedia Compound of five small rhombicuboctahedra — Type Uniform compound Index UC62 Polyhedra 5 small rhombicuboctahedra Faces 40 triangles …   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 Cube — This article is about the geometric shape. For other uses, see Cube (disambiguation). Regular Hexahedron (Click here for rotating model) Type Platonic solid Elements F = 6, E = 12 V = 8 (χ = 2) …   Wikipedia Dodecahedron — Regular Dodecahedron (Click here for rotating model) Type Platonic solid Elements F = 12, E = 30 V = 20 (χ = 2) Faces by sides 12{5} …   Wikipedia Composé polyédrique — Un composé polyédrique est un polyèdre qui est lui même composé de plusieurs autres polyèdres partageant un centre commun, l analogue tridimensionnel des composés polygonaux (en) tels que l hexagramme. Les sommets voisins d un composé… …   Wikipédia en Français Compose polyedrique — Composé polyèdrique Un composé polyèdrique est un polyèdre qui est lui même composé de plusieurs autres polyèdres partageant un centre commun, l analogue tridimensionnel des composés polygonaux tel que l hexagramme. Les sommets voisins d un… …   Wikipédia en Français Composé Polyèdrique — Un composé polyèdrique est un polyèdre qui est lui même composé de plusieurs autres polyèdres partageant un centre commun, l analogue tridimensionnel des composés polygonaux tel que l hexagramme. Les sommets voisins d un composé peuvent être… …   Wikipédia en Français 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”