What is a definition for polyhedra?

Question

What is a definition for polyhedra?

Make it basic if possible.

Answer 1

Multi-dimensional

Answer 2

A three-dimensional geometric figure whose sides are polygons. A tetrahedron, for example, is a polyhedron having four triangular sides. ◇ A regular polyhedron is a polyhedron whose faces are all congruent regular polygons. The regular tetrahedron (pyramid), hexahedron (cube), octahedron, dodecahedron, and icosahedron are the five regular polyhedrons. Regular polyhedrons are a type of Archimedean solid.

Answer 3

We can at least say that a polyhedron is built up from different kinds of element or entity, each associated with a different number of dimensions:

    * 3 dimensions: The body is bounded by the faces, and is usually the volume inside them.

    * 2 dimensions: A face is bounded by a circuit of edges, and is usually a flat (plane) region called a polygon. The faces together make up the polyhedral surface.

    * 1 dimension: An edge joins one vertex to another and one face to another, and is usually a line of some kind. The edges together make up the polyhedral skeleton.

    * 0 dimensions: A vertex (plural vertices) is a corner point.

    * -1 dimension: The nullity is a kind of non-entity required by abstract theories.

More generally in mathematics and other disciplines, "polyhedron" is used to refer to a variety of related constructs, some geometric and others purely algebraic or abstract.

A defining characteristic of almost all kinds of polyhedra is that just two faces join along any common edge. This ensures that the polyhedral surface is continuously connected and does not end abruptly or split off in different directions.

A polyhedron is a 3-dimensional example of the more general polytope in any number of dimensions.

Answer 4

A polyhedron (plural polyhedra or polyhedrons) is often defined as a geometric object with flat faces and straight edges (the word polyhedron comes from the Classical Greek πολυεδρον, from poly-, stem of πολυς, "many," + -edron, form of εδρον, "base", "seat", or "face").

This definition of a polyhedron is not very precise, and to a modern mathematician is quite unsatisfactory. Grünbaum (1994, p.43) observed that:

The Original Sin in the theory of polyhedra goes back to Euclid, and through Kepler, Poinsot, Cauchy and many others ... [in that] at each stage ... the writers failed to define what are the 'polyhedra' ...

Modern mathematicians do not even agree as to exactly what makes something a polyhedron.

Answer 5

http://www.cut-the-knot.org/do_you_know/...

Answer 6

A polyhedron is a geometric object with flat faces and straight edges

Answer 7

Any three-dimensional shape is a polyhedron. The ones in the real world don't usually have names - the recognisable names such as cube, tetrahedron, octahedron, dodecahedron and icosahedron are well known because they are mathematically interesting. In particular the ones above all have regular polygons (2D shapes) for faces.

Answer 8

Polyhedra terminology is a somewhat painful matter, to expert and novice alike. There is a certain logic to certain aspects of the long conventional names, but there is also much which is impractical, ungeneralizable, and only survives because it is entrenched. Perhaps these names are being asked to do too much: to succinctly describe the inherent properties of a polyhedron and also certain of its relationships to other polyhedra.

A polyhedron is a three dimensional shape which is bounded by regular polygons.

The five regular convex polyhedra, also known as the Platonic Solids

The five regular convex polyhedra, also known as the Platonic Solids

A regular polyhedron is a polyhedron all of whose faces are identical regular polygons, and all of whose vertices have the same number of faces around each vertex. There are only five regular convex polyhedra—polyhedra in which the all of the faces are on the outside of the polyhedron