zonohedra-package {zonohedra}

zonhedra package

Description

This package deals with zonohedra, which are zonotopes of dimension 3. It also handles zonogons (2D zonotopes) and zonosegs (1D zonotopes).

The term zonoseg ("zonotope" + "segment") is my own personal term; I could not find an alternative term. It is a linear image of the unit cube [0,1]^n in the real numbers, and a compact segment of reals.

S3 classes

Z	class(Z)
zonohedron	"zonohedron" "zonotope" "list"
zonogon	"zonogon" "zonotope" "list"
zonoseg	"zonoseg" "zonotope" "list"

For example, the section() returns very diffferent things for a zonohedron and a zonogon, and so section.zonohedron() and section.zonogon() are coded and documented separately. A section for a zonoseg does not make sense, so section.zonoseg() is undefined.

Terminology

For a convex polytope, a supporting hyperplane is a hyperplane that intersect the polytope's boundary but not its interior.
A zonotope is a convex polytope. A zonohedron has supporting planes, and a zonogon has supporting lines.

In the package zonohedra, a zonotope mean a zonotope of dimension 3, 2, or 1.

A face of a zonotope is the intersection of the boundary of the zonotope with some supporting hyperplane. A d-face is a face of dimension d. So a 0-face is a vertex, and a 1-face is an edge.

A facet of a zonotope is a face whose dimension is 1 less than the dimension of the zonotope. A facet is a maximal proper face.

A zonohedron has 0-faces (vertices), 1-faces (edges), and 2-faces (facets).

A zonogon has 0-faces (vertices) and 1-faces (edges). Since the dimension of an edge is 1 less than the dimension of the zonogon, an edge of a zonogon is also a facet of a zonogon.