In geometry, a zonohedron is a convex polyhedron that is centrally symmetric, every face of which is a polygon that is centrally symmetric (a zonogon)...

type of solids: Platonic solid, regular polyhedron, parallelohedron, zonohedron, and plesiohedron. The dual polyhedron of a cube is the regular octahedron...

each of its faces has point symmetry the truncated octahedron is a 6-zonohedron. It is also the Goldberg polyhedron GIV(1,1), containing square and hexagonal...

types of vertices surrounding this face. The rhombic icosahedron is a zonohedron, that is dual to a pentagonal gyrobicupola with regular triangular, regular...

honeycomb, but all vertices will not match. The rhombic dodecahedron is a zonohedron with twelve rhombic faces and octahedral symmetry. It is dual to the quasiregular...

It has 60 broad rhombi and 30 slim. The rhombic enneacontahedron is a zonohedron with a superficial resemblance to the rhombic triacontahedron. It can...

transformations). Since each face has point symmetry, a parallelepiped is a zonohedron. Also the whole parallelepiped has point symmetry Ci (see also triclinic)...

Rectangular cuboid Type Prism Plesiohedron Faces 6 rectangles Edges 12 Vertices 8 Properties convex, zonohedron, isogonal...

called generators. In this connection, each pair of opposite faces of a zonohedron corresponds to a crossing point of an arrangement of lines in the projective...

among the members of this family exist. The rhombic icosahedron is a zonohedron made up of 20 congruent rhombs. It can be derived from the rhombic triacontahedron...

Truncated small rhombicosidodecahedron Beveled icosidodecahedron As a zonohedron, it can be constructed with all but 30 octagons as regular polygons. It...

Catalan solid, and the dual polyhedron of the icosidodecahedron. It is a zonohedron. The ratio of the long diagonal to the short diagonal of each face is...

by Nooruddeen Durkee (then Steve Durkee), combining the words dome and zonohedron. One of the earliest models became a large climbing structure at the Lama...

Rhombohedron Type prism Faces 6 rhombi Edges 12 Vertices 8 Symmetry group Ci , [2+,2+], (×), order 2 Properties convex, equilateral, zonohedron, parallelohedron...

(equivalently, 180° rotational symmetry), the truncated icosidodecahedron is a 15-zonohedron. The name great rhombicosidodecahedron refers to the relationship with...

honeycomb. Truncated small rhombicuboctahedron Beveled cuboctahedron As a zonohedron, it can be constructed with all but 12 octagons as regular polygons. It...

up to 90 for a total of 180 degrees. The rhombic enneacontahedron is a zonohedron with a total of 90 rhombic faces: 60 broad rhombi akin to those in the...

the dual polyhedron of the cuboctahedron. The rhombic dodecahedron is a zonohedron. Its polyhedral dual is the cuboctahedron. The long face-diagonal length...

symbol {}×{}×···×{} = {}n Coxeter diagram ··· Symmetry group [2n−1], order 2n Dual polyhedron Rectangular n-fusil Properties convex, zonohedron, isogonal...

a parallelohedron; thus it is also a space-filling polyhedron, and a zonohedron. In a 1962 paper, H. S. M. Coxeter claimed that the Bilinski dodecahedron...

T and Type C Type zonohedron Face polygon rhombus Faces 132 rhombi Edges 264 Vertices 134 Symmetry group Oh, [4,3], *432 Properties convex, zonohedron...

(equivalently, 180° rotational symmetry), the truncated cuboctahedron is a 9-zonohedron. The truncated cuboctahedron can tessellate with the octagonal prism....

Every parallelohedron is a zonohedron, a centrally symmetric polyhedron with centrally symmetric faces. Like any zonohedron, it can be constructed as the...

For p < 6, the members of the sequence are omnitruncated polyhedra (zonohedrons), shown below as spherical tilings. For p > 6, they are tilings of the...

some stellation is a faceting of the dual to the original polyhedron. A zonohedron is a convex polyhedron in which every face is a polygon that is symmetric...

group D3, [2,3]+, (223), order 6 Dual polyhedron trigonal antiprism Properties convex, equilateral polygon, face-transitive, zonohedron, parallelohedron...

(zōnnúnai), ζώνη (zṓnē), ζωστήρ (zōstḗr), ζῶστρον phylozone, zonal, zone, zonohedron, zonotope, zoster zyg- (ΖΥΓ) yoke Greek ζευγνύναι (zeugnúnai), ζεῦγμα...

revolution. Convex polyhedra with rhombi include the infinite set of rhombic zonohedrons, which can be seen as projective envelopes of hypercubes. A rhombohedron...

dodecahedron Rhombo-hexagonal dodecahedron Truncated trapezohedron Deltahedron Zonohedron Prismatoid Cupola Bicupola Dihedron Hosohedron Convex uniform honeycomb...

cC have an even number of sides and are centrally symmetric, it is a zonohedron: The chamfered cube is also the Goldberg polyhedron GPIV(2,0) or {4+,3}2...