Zonohedron - Wikipedia
In the case of a zonohedron, the edges surrounding each face can be grouped into pairs of parallel edges, and when translated via the Gauss map any such pair becomes a pair of contiguous segments on the same great circle.
Zonohedron -- from Wolfram MathWorld
2024年11月26日 · Consider any star of n line segments through one point in space such that no three lines are coplanar. Then there exists a polyhedron, known as a zonohedron, whose faces consist of n(n-1) rhombi and whose edges are parallel to the n given lines in sets of 2(n-1).
Zonohedron - Encyclopedia of Mathematics
2014年4月10日 · Any zonohedron is the projection of a cube of sufficiently high dimension. A special role is assigned in the class of centrally-symmetric convex bodies to zonoids — limiting cases of zonohedra; they admit a specific integral representation of the support function and are finite-dimensional sections of the sphere in the Banach space $L_1$.
Zonotopes - cran.csail.mit.edu
2024年7月6日 · A zonohedron has 0-faces (vertices), 1-faces (edges), and 2-faces (facets). All the facets are zonogons. A parallelogram facet is called trivial, and facets with more than 4 edges are non-trivial.
Zonohedra - George W. Hart
A zonohedron (by one restrictive definition) is a convex polyhedron all of whose faces are parallelograms. (less restrictive definitions, below, allow other types of faces.)
Polar zonohedra - Steve Dutch
The three-fold zonohedron is a rhombohedron, of which a cube is a special case. One special case of the four-fold zonohedron is the rhombic dodecahedron. But if the polyhedron is stretched a bit so the equatorial faces are squares, the top and bottom sets of faces are 60-120 rhombuses.
The Geometry Junkyard: Zonohedra - Donald Bren School of …
A zonohedron is a polyhedron in which every face is centrally symmetric. Zonohedra can be defined in various ways, for instance as the Minkowski sums of line segments. The combinatorics of their faces are equivalent to those of line arrangements in the plane.
zonohedron - Wolfram|Alpha
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The present paper answers the following question: What shape does the polar zonohedron approach when n tends to infinity? 2. Zonohedra. A zonohedron is a convex polyhedron whose faces are cen-trally symmetrical polygons, e.g., parallelograms. Every edge determines a zone.
We define a generalized zonohedron to be a polyhedron (in R3) such that each face has an even number of edges and on each face, each edge is parallel to its opposite edge; an example is in Figure 1.
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