ZONOHEDRON Meaning and
Definition
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A zonohedron is a three-dimensional geometric shape or polyhedron that has planar polygonal faces. More specifically, it is a convex polyhedron whose faces consist of parallelograms. These parallelograms are congruent and lie in parallel planes. The sides of the parallelograms correspond to the edges of the zonohedron, and the corners of the parallelograms are the vertices of the zonohedron.
Zonohedra exhibit certain symmetries that make them visually appealing. They possess some form of rotational symmetry, such that they can be rotated by a specific angle and still retain their original shape. This rotational symmetry is often accompanied by translational symmetry, where the zonohedron can be translated in multiple directions without changing its overall appearance.
These polyhedra are named after the concept of a "zone" – an area bounded by planes that intersect a convex polyhedron. The faces of a zonohedron correspond to these intersecting planes. Zonohedra can have differing numbers of faces, edges, and vertices, resulting in various distinct types. Examples of zonohedra include the cube (hexahedron), rhombic dodecahedron, rhombic triacontahedron, and many others.
Zonohedra find applications in areas such as crystallography, architecture, and computational geometry due to their interesting geometric properties and symmetries. Their unique structure makes them an intriguing subject of study in the field of mathematics and geometry.
Etymology of ZONOHEDRON
The word "zonohedron" has a Greek origin. It is derived from two Greek words: "zónē" meaning "belt" or "zone", and "hedra" meaning "base" or "seat". When combined, "zonohedron" can be understood as a three-dimensional shape with zones or belts as its defining characteristic. The term was coined by the mathematician H. S. M. Coxeter in 1951 to describe certain geometric polyhedra.
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