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Polyhedron

Biography

In geometry, a polyhedron (pl.: polyhedra or polyhedrons; from Greek πολύ (poly-) 'many' and ἕδρον (-hedron) 'base, seat') is a three-dimensional figure with flat polygonal faces, straight edges and sharp corners or vertices. The term "polyhedron" may refer either to a solid figure or to its boundary surface. The terms solid polyhedron and polyhedral surface are commonly used to distinguish the two concepts. Also, the term polyhedron is often used to refer implicitly to the whole structure formed by a solid polyhedron, its polyhedral surface, its faces, its edges, and its vertices. There are many definitions of polyhedra, not all of which are equivalent. Under any definition, polyhedra are typically understood to generalize two-dimensional polygons and to be the three-dimensional specialization of polytopes (a more general concept in any number of dimensions). Polyhedra have several general characteristics that include the number of faces, topological classification by Euler characteristic, duality, vertex figures, surface area, volume, interior lines, Dehn invariant, and symmetry. A symmetry of a polyhedron means that the polyhedron's appearance is unchanged by a transformation, such as rotating and reflecting. Convex polyhedra are a well-defined class of polyhedra with several equivalent standard definitions. Every convex polyhedron is the convex hull of its vertices, and the convex hull of a finite set of points is a polyhedron. Many common families of convex polyhedra, with cubes and pyramids are familiar examples of such. There exist many miscellaneous families of polyhedra. Space-filling polyhedra are those that can be packed together with copies of themselves or with other different types of polyhedra in three-dimensional space. Flexible polyhedra are the polyhedra that can change their overall shape while preserving the shapes of their faces; some have such. Ideal polyhedron is a convex polyhedron defined in three-dimensional hyperbolic space. Lattice po

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Discography

Records they worked on — most-collected first.

Credited work

29 releases · 10 albums · active 2003–2014

  • Production · 34
  • Engineering · 4
  • Performance · 2
  • Mastering · 1

Studios: I-Level · Fort Knocs Studios · Truestar Studios · The Poolroom

Frequent collaborators

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