zonohedron-getmetrics: Get Important Metrics about a Zonohedron, and Print and...

In zonohedra: Compute and Plot Zonohedra from Vector Generators

Get Important Metrics about a Zonohedron, and Print and Summarize Them

Description

Get some important zonohedron metrics; for most some computation is needed.

The print() function prints nicely formatted facts about a zonohedron, including its matroid.

The summary() function prints a single-line summary, formatted as a row in a data frame.

Usage

## S3 method for class 'zonohedron'
getmetrics( x )

## S3 method for class 'zonohedron'
print( x, trans2=FALSE, matroid=TRUE, ... )

## S3 method for class 'zonohedron'
summary( object, ... )

Arguments

x	a zonohedron object as returned by the constructor zonohedron()
trans2	if TRUE then print extra metrics on the 2-transition surface associated with x
matroid	if TRUE then print extra information about the matroid associated with x
object	a zonohedron object as returned by the constructor zonohedron()
...	for print() further arguments are ignored; for summary() the further arguments can be *more* zonohedron objects, which are summarized by adding more rows to the same data frame; see Examples.

Value

getmetrics.zonohedron() returns a list with these items:

vertices	the number of vertices
edges	the number of edges
facets	the number of facets (2D faces); all of them are zonogons
area	the sum of the areas of all the facets
volume	as a polytope

All of these are always positive.

print.zonohedron() returns TRUE or FALSE.

summary.zonohedron() returns a data frame, see Examples.

See Also

genlist, zonohedron(),

Examples

zono = zonohedron( classics.genlist[['BD']] )
zono
# zonohedron:
# fullname:                          Bilinski dodecahedron 
# generators (original):             4 
# generators with multiples:         0 
# generators (simplified):           4 
# number of facets:                  12  [6 antipodal facet-pairs]
# facets that contain 0:             4    { 1 3 4 6 }
# number of edges:                   24 
# center:                            0.809017 2.118034 1.309017 
# pointed:                           TRUE 
# salient:                           TRUE 
# area:                              38.83282 
# volume:                            16.94427 
# 
# matroid:
# ground set:           4 points   {1 2 3 4}
# hyperplanes:          6     {1 2}  {1 3}  {1 4}  {2 3}  {2 4}  {3 4}
# rank:                 3
# loops:                0   {}
# multiple groups:      0   {}
# uniform:              TRUE
# paving:               TRUE
# simple:               TRUE
# This matroid is constructed from a 3x4 real matrix.
#             1        2        3         4
# [1,] 1.000000 1.618034 0.000000 -1.000000
# [2,] 1.618034 0.000000 1.000000  1.618034
# [3,] 0.000000 1.000000 1.618034  0.000000


summary( zono )
#                fullname generators vertices edges facets     area   volume
# 1 Bilinski dodecahedron          4       14    24     12 38.83282 16.94427

zono4 = zonohedron( classics.genlist[['RI']] )
zono7 = zonohedron( classics.genlist[['TO']] )
summary( zono, zono4, zono7 )
#                fullname generators vertices edges facets     area   volume
# 1 Bilinski dodecahedron          4       14    24     12 38.83282 16.94427
# 2   rhombic icosahedron          5       22    40     20 64.72136 42.36068
# 3  truncated octahedron          6       24    36     14 53.56922 32.00000

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