Compound of three cubes

Compound of three cubes
Type	Uniform compound
Index	UC8
Convex hull	Nonuniform truncated octahedron
Polyhedra	3 cubes
Faces	6+12 squares
Edges	36
Vertices	24
Symmetry group	octahedral (Oh)
Subgroup restricting to one constituent	4-fold prismatic (D4h)

This uniform polyhedron compound is a symmetric arrangement of 3 cubes, considered as square prisms. It can be constructed by superimposing three identical cubes, and then rotating each by 45 degrees about a separate axis (that passes through the centres of two opposite faces).

This compound famously appears in the lithograph print Waterfall by M.C. Escher.

Cartesian coordinates

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

(±√2, 0, ±1)

References

• Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society 79: 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 The Island Hymn Chamber of Local Authorities Look at other dictionaries: Compound of six cubes with rotational freedom — Type Uniform compound Index UC7 Polyhedra 6 cubes Faces 12+24 squares …   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 twelve tetrahedra with rotational freedom — Type Uniform compound Index UC2 Polyhedra 12 tetrahedra Faces 48 triangles …   Wikipedia Compound of six tetrahedra with rotational freedom — Type Uniform compound Index UC1 Polyhedra 6 tetrahedra Faces 24 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 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 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 Waterfall (M. C. Escher) — Artwork title=Waterfall artist=M. C. Escher year=1961 type=lithograph height=38 width=30 Waterfall is a lithograph print by the Dutch artist M. C. Escher which was first printed in October, 1961. It shows an apparent paradox where water from the… …   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 Small complex rhombicosidodecahedron — Type Uniform star polyhedron Elements F = 62, E = 120 (60x2) V = 20 (χ = 38) Faces by sides 20{3}+12{5/2}+30{4} …   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”