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.
# S3 method for zonohedron
getmetrics( x )# S3 method for zonohedron
print( x, trans2=FALSE, matroid=TRUE, ... )
# S3 method for zonohedron
summary( object, ... )
getmetrics.zonohedron() returns a list with these items:
the number of vertices
the number of edges
the number of facets (2D faces); all of them are zonogons
the sum of the areas of all the facets
as a polytope
All of these are always positive.
print.zonohedron() returns TRUE or FALSE.
summary.zonohedron() returns a data frame, see Examples.
a zonohedron object as returned by the constructor zonohedron()
if TRUE then print extra metrics on the 2-transition surface associated with x
if TRUE then print extra information about the matroid associated with x
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.
genlist,
zonohedron(),
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
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