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Polyhedron Database Documentation

History

Created : Salix alba (talk) 11:53, 4 February 2006 (UTC)
Copied documentation here (from Template talk:Polyhedra DB) and updated/cleaned up a bit: Tom Ruen 11:42, 30 December 2006 (UTC)

Purpose

{{Template:XXX polyhedra db}} — A database of information about different polyhedra.

Usage

{{Uniform polyhedra db
  |Template used to display the information #REQUIRED
  |Short form name #REQUIRED
}}

Display templates

The first argument to the template tag should be the name of a second template used to display information about an individual polyhedron. Possible arguments are

Template talk:Polyhedra smallbox2: Displays the polyhedron in a small box, intended to be used inside a table

Short names of Polyhedron

The nameing system follows the names used for the polyhedron but they have been shortend.

T - tetrahedron or Tetra
O - octahedron or Octa
C - Cube
D - Dodecahedron or Dodeca
I - Icosahedron or Icosi
r - rhombi
s - stelated
g - great
t - truncated
l - small (lesser) used to avoid naming conflict
d - ditrigonal
h - hemi
u - uniform
n - snub (n is used to avoid name conflict)

So gtCO becomes great truncated CubeOctahedron.

Properties defined

For each polyhedron the following properties are defined.

Note: Each database template file can have slightly different data-fields, depending on what makes sense:

Here the initial T is replaced by the name of the each polyhedron

T-name=Tetrahedron - the name used in wikipedia for the polyhedron
stH-altname1=Quasitruncated hexahedron - alternate name for the polyhedron (optional)
stH-altname2=stellatruncated cube - second alternate name (optional)
T-image=tetrahedron.jpg - image of the polyhedron
T-Wythoff=3|3 2 - Wythoff symbol
T-W=1 - number used in Polyhedron Models, by Magnus Wenninger.
T-U=01 - Uniform indexing: U01-U80 (Tetrahedron first, Prisms at 76+)
T-K=06 - Kaleido indexing: K01-K80 <K(n)=U(n-5) for n=6..80> (prisms 1-5, Tetrahedron 6+)
T-C=15 - Number used in Coexeter et al -
T-V=4 - Number of vertices
T-E=6 - Number of edges
T-F=4 - Number of faces
T-Fdetail=4{3} - Number{type} of faces
T-chi=2 - Euler charteristic
T-vfig=3.3.3 - Vertex figure
T-vfigimage=tetrahedron_vertfig.png - image of vertex figure
T-group=T_d - Symmetry group
T-B=Tet - Bowers name

Example

Code	Result
{{Reg polyhedra db\|Polyhedra smallbox2\|T}}	Tetrahedron Tet V 4,E 6,F 4=4{3} χ=2, group=T_d, A₃, [3,3], (*332) 3 \| 2 3 \| 2 2 2 - 3.3.3 W1, U01, K06, C15

How it works

Each polyhedron is included with code like

{{Reg polyhedra db|Polyhedra smallbox2|T}}

Where Reg polyhedra db is a template containg the regular polyhedron data. Polyhedra smallbox2 is a template for displaying the data and T is the name of the polyhedra, in this case Tetrahedron.

Template:Reg polyhedra db is like

{{{{{1}}}|{{{2}}}|

|T-name=Tetrahedron|T-image=tetrahedron.jpg|T-Wythoff=3|3 2|
|T-W=1|T-U=01|T-K=06|T-C=15|T-V=4|T-E=6|T-F=4|T-Fdetail=4{3}|T-chi=2|
|T-vfig=3.3.3|T-vfigimage=tetrahedron_vertfig.png|T-group=T<sub>d</sub>|

|O-name=Octahedron|O-image=octahedron.jpg|O-Wythoff=4|3 2|
...
}}

The first two parameters to this template just pass their arguments through, so this resolves to

{{Polyhedra smallbox2|T|T-name=Tetrahedron|....}}

and means that the Polyhedra smallbox2 template is called. Each variable in this template is of the form X-name where X is a short name for the polyhedron.

Template:Polyhedra smallbox2 is like

[[Image:{{{{{{1}}}-image}}}|100px]]<BR>
[[{{{{{{1}}}-name}}}]]<BR>
V {{{{{{1}}}-V}}},E {{{{{{1}}}-E}}},F {{{{{{1}}}-F}}}={{{{{{1}}}-Fdetail}}}
<br>''?''={{{{{{1}}}-chi}}}, group={{{{{{1}}}-group}}}
<BR>{{{{{{1}}}-Wythoff}}} - {{{{{{1}}}-vfig}}}
<BR>W{{{{{{1}}}-W}}}, U{{{{{{1}}}-U}}}, K{{{{{{1}}}-K}}}, C{{{{{{1}}}-C}}}
<br>{{{{{{1}}}-altname|}}}

Occurences of {{{1}}} are replaced by the first parameter. In this case T so after substituting the variable it becomes

[[Image:{{{T-image}}}|100px]]<BR>
[[{{{T-name}}}]]<BR>
V {{{T-V}}},E {{{T-E}}},F {{{T-F}}}={{{T-Fdetail}}}
<br>''?''={{{T-chi}}}, group={{{T-group}}}
<BR>{{{{T-Wythoff}}} - {{{T-vfig}}}
<BR>W{{{{T-W}}}, U{{{T-U}}}, K{{{T-K}}}, C{{{T-C}}}
<br>{{{T-altname|}}}

Finally {{{T-image}}} and {{{T-name}}} just select the other parameters from the Reg polyhedra db so this now just like an infobox template.