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zonohedron
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zonohedron

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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. Fedorov, a Russian crystallographer. More generally, in any dimension, the Minkowski sum of line segments forms a polytope known as a zonotope.

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Encyclopedic overview

11 sections
Contents
  • Tiling space
  • From Minkowski sums
  • From arrangements
  • Types
  • Dissections
  • Zonohedrification
  • Zonotopes
  • Volume
  • See also
  • References
  • External links

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. Fedorov, a Russian crystallographer. More generally, in any dimension, the Minkowski sum of line segments forms a polytope known as a zonotope.

== Tiling space ==

Excerpted from Wikipedia’s “zonohedron” article, available under the CC BY-SA 4.0 licence.

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