Math 2.0

Convex and discrete geometry Definition

Polyhedron

Builds on Convex hullPlane

Definition

A convex polyhedron is the convex hull of a finite set of points of ℝ3\mathbb{R}^3 that do not all lie in one plane. A polyhedron is a bounded subset of ℝ3\mathbb{R}^3 with a connected interior that is the union of finitely many convex polyhedra. Its faces are the connected parts of its boundary inside the planes that cover the boundary. Its edges and vertices are the segments and points where the faces meet.

Remarks

There is no single definition of a polyhedron that all authors use. Some definitions describe a surface in place of a solid, and some allow self-crossing faces. A convex polyhedron is also a bounded intersection of finitely many closed half-spaces, with a nonempty interior. Examples are the cube, the regular tetrahedron and each prism over a convex polygon.

Reading path

To understand this page from the ground up, read these 3 pages in order. The foundations come first.

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Convex hull, concept, no evidence levelConvex hullconceptPlane, concept, no evidence levelPlaneconceptPolyhedron, definition, no evidence levelPolyhedrondefinition
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  1. Convex hull concept
  2. Plane concept
  3. Polyhedron definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Polyhedron, Definition
  2. Web https://en.wikipedia.org/wiki/Polyhedron, lead section
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DefinesPolyhedron
UsesConvex hull, Plane

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