Author Question: What is a definition for polyhedra? (Read 1060 times)

Jesse_J

  • Sr. Member
  • ****
  • Posts: 282
What is a definition for polyhedra?
Make it basic if possible.



j_sun

  • Sr. Member
  • ****
  • Posts: 384
Reply #1 on: Jun 18, 2013
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.



Related Topics

Need homework help now?

Ask unlimited questions for free

Ask a Question

hummingbird

  • Sr. Member
  • ****
  • Posts: 324
Reply #2 on: Jun 18, 2013
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.



Millan

  • Sr. Member
  • ****
  • Posts: 368
Reply #3 on: Jun 18, 2013
A polyhedron is a geometric object with flat faces and straight edges



j_sun

  • Sr. Member
  • ****
  • Posts: 384
Reply #4 on: Jun 18, 2013
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.



Melanie

  • Full Member
  • ***
  • Posts: 204
Reply #5 on: Jun 18, 2013
Multi-dimensional



hummingbird

  • Sr. Member
  • ****
  • Posts: 324
Reply #6 on: Jun 18, 2013
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



 

Did you know?

One way to reduce acid reflux is to lose two or three pounds. Most people lose weight in the belly area first when they increase exercise, meaning that heartburn can be reduced quickly by this method.

Did you know?

When blood is exposed to air, it clots. Heparin allows the blood to come in direct contact with air without clotting.

Did you know?

It is important to read food labels and choose foods with low cholesterol and saturated trans fat. You should limit saturated fat to no higher than 6% of daily calories.

Did you know?

The top five reasons that children stay home from school are as follows: colds, stomach flu (gastroenteritis), ear infection (otitis media), pink eye (conjunctivitis), and sore throat.

Did you know?

The use of salicylates dates back 2,500 years to Hippocrates’s recommendation of willow bark (from which a salicylate is derived) as an aid to the pains of childbirth. However, overdosage of salicylates can harm body fluids, electrolytes, the CNS, the GI tract, the ears, the lungs, the blood, the liver, and the kidneys and cause coma or death.

For a complete list of videos, visit our video library