symmetrize: symmetrize a zonotope

In zonohedra: Compute and Plot Zonohedra from Vector Generators

symmetrize a zonotope

Description

The input is a zonotope whose matroid is simple. The function adds new generators that creates a new zonotope that is a translate of the original, and has center of symmetry at 0.

Usage

## S3 method for class 'zonotope'
symmetrize( x, e0=0, e1=1.e-6, e2=1.e-10, ... )

Arguments

x	a zonotope object - a zonohedron, a zonogon, or a zonoseg. The matroid of this zonotope must be simple.
e0	see zonohedron()
e1	see zonohedron()
e2	see zonohedron()
...	not used

Details

Each generator g (a column of the matrix) is replace by 2 generators: g/2 and -g/2. The new set of generators correponds to a star at 0, from Sec 2-8 of Coxeter.
The new ground points are obtained by translating the original ground points by the their maximum.

Value

The function returns a zonotope that is a translate of the original, and has center of symmetry at 0.
In case of error, the function returns NULL.

References

Coxeter, H.S.M. Regular Polytopes. Dover Publications. 1973.

See Also

zonohedron(), zonogon(), zonoseg()

zonohedra documentation built on Sept. 1, 2025, 9:08 a.m.