Template:Infobox polytope/doc

From Polytope Wiki
Jump to navigation Jump to search

Usage[edit source]

{{Infobox polytope
| name            = (Takes article name by default)
| img             = Image file name
| 3d              = 3D model file name
| off             = OFF file name
| rank            = Rank
| dim             = If provided with rank it is added as the dimension row. If provided alone it appears as the rank. Fill both this and rank only if they differ.
| type            = General type
| space           = Space (spherical, euclidean, hyperbolic)
| bsa             = Bowers style acronym
| cd              = Coxeter-Dynkin diagram
| schlafli        = Schläfli symbol
| schläfli type   = Schläfli type. Omit this if it is identical to the Schläfli symbol.
| configsym       = Configuration symbol. Omit this for tame polygons.
| symmetry        = Symmetry group
| army            = Army
| reg             = Regiment
| company         = Company
| verf            = Vertex figure(s)
| verf2 ...
| ...
| petrie-polygons = Petrie polygon count and types
| netcount        = Number of nets
| components      = Component count and types
| facets          = Facet count and types. Use only when the infobox is for a family of polytopes of variable rank
| ridges          = Ridge count and types. Use only when the infobox is for a family of polytopes of variable rank
| peaks           = Peak count and types. Use only when the infobox is for a family of polytopes of variable rank
| spires          = Spire count and types. Use only when the infobox is for a family of polytopes of variable rank
| ...
| tera            = Teron count and types
| cells           = Cell count and types
| faces           = Face count and types
| edges           = Edge count
| vertices        = Vertex count
| custom_measure  = Use when measures are not in terms of edge length
| edge_lengths    = Edge lengths (in measures header)
| el              = Edge lengths (as measure)
| el2 ...
| rad             = Circumradius
| rad1            = Edge radius
| rad2            = Face radius
| ...
| inrad           =
| hvol            = Polytope hypervolume
| vol             = Polyhedron volume
| area            = Polygon area
| len             = Polytelon length
| ...
| diteral         = Diteral angle(s)
| diteral2 ...
| dichoral        = Dichoral angle(s)
| dichoral2 ...
| dihedral        = Dihedral angle(s)
| dihedral2 ...
| angle           = Polygon angle(s)
| angle2 ...
| h               = Height
| h2 ...
| dual            = Dual polytope
| petrial         = Petrie dual
| halving         = Halving
| skewing         = Skewing
| conj            = Conjugate polytope
| core            = Convex core
| conv            = Is convex (Yes/No)
| chiral          = Is chiral (Yes/No)
| genus           = The genus if a polyhedron.  Defaults to 0 for convex polyhedron.
| bn               = The n th Betti number. Include only if non-zero and if the rank exceeds n+1 .
| skeleton        = The 2-skeleton.'
| orient          = Is orientable (Yes/No)
| doublecover     = Its orientation double cover if it is not orientable.
| nat             = Nature (Tame/Feral/Wild) 
| dv              = Dimension vector. Omit this if the polytope is planar. 
}}


Advanced options[edit source]

|suppress_missing_measures = Does not add the page to Category:Pages with missing measures. To be used only when any of the missing fields (circumradius, difacetal angles, hypervolume) do not apply to the polytope at hand, or when the formulae for the measures do not fit on the infobox and are given elsewhere on the article.
|suppress_missing_off = Does not add the page to Category:Pages without OFF files. To be used only when the page does not describe or focus on a single polytope (up to isometries and scaling), or when the OFF file format doesn't permit the shape at hand to be represented.
|suppress_missing_orientability = Does not add the page to a missing orientability category. To be used only when the page describes a configuration or a compound.

Example[edit source]

Icosahedron
Rank3
TypeRegular
Notation
Bowers style acronymIke
Coxeter diagramx3o5o ()
Schläfli symbol{3,5}
Conway notationI
Stewart notationI5
Elements
Faces20 triangles
Edges30
Vertices12
Vertex figurePentagon, edge length 1
Petrie polygons6 skew decagons
Holes12 pentagons
Measures (edge length 1)
Circumradius
Edge radius
Inradius
Volume
Surface area
Dihedral angle
Central density1
Number of external pieces20
Level of complexity1
Related polytopes
ArmyIke
RegimentIke
DualDodecahedron
Petrie dualPetrial icosahedron
φ 2 Great dodecahedron
κ ?Petrial small stellated dodecahedron
ConjugateGreat icosahedron
Abstract & topological properties
Flag count120
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryH3, order 120
Flag orbits1
ConvexYes
Net count43380
NatureTame

The code below results in the infobox on the right:

{{Infobox polytope
|name      = Icosahedron
|image     = Icosahedron.png
|3d        = Icosahedron.stl
|off       = Icosahedron.off
|rank      = 3
|type      = [[Regular]]
|obsa      = {{BSAhelp|Ike}}
|schlafli  = {{Schlafli|3|5|cat=yes}}
|conway    = I
|stewart   = {{Stew|I5}}
|coxeter   = {{ACD|x3o5o|both=yes}}
|symmetry  = [[Dodecahedral symmetry|H<sub>3</sub>]], order 120
|orbits    = 1
|army      = '''Ike'''
|reg       = '''Ike'''
|faces     = 20 [[triangle]]s
|edges     = 30
|vertices  = 12
|verf      = [[Pentagon]], edge length 1
|circum    = <math>\sqrt{\frac{5+\sqrt5}{8}} \approx 0.95106</math>
|rad1      = <math>\frac{1+\sqrt5}{4} \approx 0.80902</math>
|inrad     = <math>\frac{3\sqrt3+\sqrt{15}}{12} \approx 0.75576</math>
|volume    = <math>5\frac{3+\sqrt5}{12} \approx 2.18169</math>
|surface   = <math>5\sqrt{3} \approx 8.660254</math>
|dih       = <math>\arccos\left(-\frac{\sqrt5}{3}\right) \approx 138.18969^\circ</math>
|flags     = 120
|netcount  = 43380
|pieces    = 20
|loc       = 1
|petp      = 6 [[skew]] [[decagon]]s
|holes     = 12 [[pentagon]]s
|dual      = [[Dodecahedron]]
|petrial   = [[Petrial icosahedron]]
|phi2      = [[Great dodecahedron]]
|kappa     = [[Petrial small stellated dodecahedron]]
|conj      = [[Great icosahedron]]
|conv      = Yes
|orient    = Yes
|nat       = Tame
}}