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). Any zonohedron may equivalently be described as the Minkowski sum of a set of line segments in three-dimensional space, or as a three-dimensional projection of a hypercube. Zonohedra were originally defined and studied by E. S. Fedorove, a Russian crystallographer. More generally, in any dimension, the Minkowski sum of line segments forms a polytope known as a zonotope.
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)...
parallelepiped, an equilateral cuboid, a right rhombohedron, and a 3-zonohedron. It is a regular square prism in three orientations, and a trigonal trapezohedron...
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...
Truncated small rhombicosidodecahedron Beveled icosidodecahedron As a zonohedron, it can be constructed with all but 30 octagons as regular polygons. It...
transformations). Since each face has point symmetry, a parallelepiped is a zonohedron. Also the whole parallelepiped has point symmetry Ci (see also triclinic)...
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...
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...
(equivalently, 180° rotational symmetry), the truncated icosidodecahedron is a 15-zonohedron. The name great rhombicosidodecahedron refers to the relationship with...
It has 60 broad rhombi and 30 slim. The rhombic enneacontahedron is a zonohedron with a superficial resemblance to the rhombic triacontahedron. It can...
honeycomb. Truncated small rhombicuboctahedron Beveled cuboctahedron As a zonohedron, it can be constructed with all but 12 octagons as regular polygons. It...
(equivalently, 180° rotational symmetry), the truncated cuboctahedron is a 9-zonohedron. The truncated cuboctahedron can tessellate with the octagonal prism....
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...
the dual polyhedron of the cuboctahedron. The rhombic dodecahedron is a zonohedron. Its polyhedral dual is the cuboctahedron. The long face-diagonal length...
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...
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...
each line segment. Every face of a zonohedron is a zonogon, and every zonogon is the face of at least one zonohedron, the prism over that zonogon. Additionally...
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...
Every parallelohedron is a zonohedron, a centrally symmetric polyhedron with centrally symmetric faces. Like any zonohedron, it can be constructed as the...
revolution. Convex polyhedra with rhombi include the infinite set of rhombic zonohedrons, which can be seen as projective envelopes of hypercubes. A rhombohedron...
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...
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