Author Question: What is a definition for polyhedra? (Read 1669 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?

Asthma-like symptoms were first recorded about 3,500 years ago in Egypt. The first manuscript specifically written about asthma was in the year 1190, describing a condition characterized by sudden breathlessness. The treatments listed in this manuscript include chicken soup, herbs, and sexual abstinence.

Did you know?

A recent study has found that following a diet rich in berries may slow down the aging process of the brain. This diet apparently helps to keep dopamine levels much higher than are seen in normal individuals who do not eat berries as a regular part of their diet as they enter their later years.

Did you know?

Signs of depression include feeling sad most of the time for 2 weeks or longer; loss of interest in things normally enjoyed; lack of energy; sleep and appetite disturbances; weight changes; feelings of hopelessness, helplessness, or worthlessness; an inability to make decisions; and thoughts of death and suicide.

Did you know?

Though “Krazy Glue” or “Super Glue” has the ability to seal small wounds, it is not recommended for this purpose since it contains many substances that should not enter the body through the skin, and may be harmful.

Did you know?

GI conditions that will keep you out of the U.S. armed services include ulcers, varices, fistulas, esophagitis, gastritis, congenital abnormalities, inflammatory bowel disease, enteritis, colitis, proctitis, duodenal diverticula, malabsorption syndromes, hepatitis, cirrhosis, cysts, abscesses, pancreatitis, polyps, certain hemorrhoids, splenomegaly, hernias, recent abdominal surgery, GI bypass or stomach stapling, and artificial GI openings.

For a complete list of videos, visit our video library