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Documentation - Discussion

[edit] Documentation

[edit] Purpose

{{polyhedra DB}} — A database of information about different polyhedra.

[edit] Usage

{{Polyhedra DB
  |Template used to display the information #REQUIRED
  |Short form name #REQUIRED
}}

[edit] 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

[edit] Short names of Polyhedron

The naming 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.

[edit] Properties defined

For each polyhedron the following properties are defined.

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

[edit] Example

Code	Result
{{Polyhedra DB|Polyhedra smallbox2|T}}	Tetrahedron Tet V 4,E 6,F 4=4{3} χ=2, group=Td 3 | 3 2 - 3.3.3 W1, U01, K06, C15

[edit] Full list of names available

• T - Tetrahedron - Tet
• O - Octahedron - Oct
• C - Hexahedron - Cube
• I - Icosahedron - Ike
• D - Dodecahedron - Doe
• gI - Great icosahedron - Gike
• gD - Great dodecahedron - Gad
• lsD - Small stellated dodecahedron - Sissid
• gsD - Great stellated dodecahedron - Gissid
• CO - Cuboctahedron - Co
• ID - Icosidodecahedron - Id
• gID - Great icosidodecahedron - Gid
• DD - Dodecadodecahedron - Did
• ldID - Small ditrigonal icosidodecahedron - Sidtid
• dDD - Ditrigonal dodecadodecahedron - Ditdid
• gdID - Great ditrigonal icosidodecahedron - Gidtid
• tT - Truncated tetrahedron - Tut
• tO - Truncated octahedron - Toe
• tC - Truncated cube - Tic
• tI - Truncated icosahedron - Ti
• tD - Truncated dodecahedron - Tid
• tgD - Truncated great dodecahedron - Tigid
• gtI - Truncated great icosahedron - Tiggy
• stH - Stellated truncated hexahedron - Quith
• lstD - Small stellated truncated dodecahedron - Quitsissid
• gstD - Great stellated truncated dodecahedron - Quitgissid
• ThH - Tetrahemihexahedron - Thah
• OhO - Octahemioctahedron - Oho
• ChO - Cubohemioctahedron - Cho
• lIhD - Small icosihemidodecahedron - Seihid
• lDhD - Small dodecahemidodecahedron - Sidhid
• gIhD - Great icosihemidodecahedron - Geihid
• gDhD - Great dodecahemidodecahedron - Gidhid
• gDhI - Great dodecahemicosahedron - Gidhei
• lDhI - Small dodecahemicosahedron - Sidhei
• lrCO - Small rhombicuboctahedron - Sirco
• lCCO - Small cubicuboctahedron - Socco
• ugrCO - Uniform great rhombicuboctahedron - Querco
• lrID - Small rhombicosidodecahedron - Srid
• lDID - Small dodecicosidodecahedron - Saddid
• ugrID - Uniform great rhombicosidodecahedron - Qrid
• gIID - Great icosicosidodecahedron - Giid
• ldDID - Small ditrigonal dodecicosidodecahedron - Sidditdid
• IDD - Icosidodecadodecahedron - Ided
• grCO - Great rhombicuboctahedron - Girco
• gtCO - Great truncated cuboctahedron - Quitco
• ctCO - Cubitruncated cuboctahedron - Cotco
• grID - Great rhombicosidodecahedron - Grid
• gtID - Great truncated icosidodecahedron - Gaquatid
• itDD - Icositruncated dodecadodecahedron - Idtid
• tDD - Truncated dodecadodecahedron - Quitdid
• lrH - Small rhombihexahedron - Sroh
• grH - Great rhombihexahedron - Groh
• rI - Rhombicosahedron - Ri
• grD - Great rhombidodecahedron - Gird
• gDI - Great dodecicosahedron - Giddy
• lrD - Small rhombidodecahedron - Sird
• lDI - Small dodecicosahedron - Siddy

[edit] How it works

Each polyhedron is included with code like

{{Polyhedra DB|Polyhedra smallbox2|T}}

Where Polyhedra DB is a template containg all the data. Polyhedra smallbox2 is a template for displaying the data and T is the name of the polyhedra, in this case Tetrahedron.

Template: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>''χ''={{{{{{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>''χ''={{{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 Polyhedra DB so this now just like an infobox template.

[edit] See also

[edit] History

Created 

Salix alba (talk) 11:53, 4 February 2006 (UTC)

[edit] Discussion

[edit] Template:Infobox Polyhedron with vertfig

Okay, I understand a little better seeing Template:Polyhedra DB. How about trying a test interacting with Template:Infobox Polyhedron with vertfig. Sorry I dare not try yet myself.

I think a big step left is to define a set of similar templates like this for varied types of polyhedra which will have slightly different useful information, even if we may want all under the same DB construction.

Tom Ruen 21:29, 31 January 2006 (UTC)

Yep should not be a problem. Its easy enough to use the same scheme with a different database of info and a different display method. I'll get on with vertex figure soon. I'm also interested in trying those with the same spherical triangles. --Salix alba (talk) 00:02, 1 February 2006 (UTC)

If you're interested in spherical triangles, and have Windows, check out a cool program for reflection symmetry at least.

http://geometrygames.org/KaleidoTile/index.html

It allows you to select a symmetry type and it draws a fundamental triangle and you can pick a point inside and it divides the triangle into 3 regions, colored differently, and it generates all the uniform polyehedral, including tilings and (a few) hyperbolic tilings. I mean there's 7 main "control points" for regulars/semiregulars, and any smoothly between as well.

It is also interesting to see some tilings come up in different symmetry modes, showing for example an octahedron has both Oh and Th symmetry.

Well a good exploratory tool at least.

Oh, apparently called Schwarz triangle for spheres.

• http://mathworld.wolfram.com/SchwarzTriangle.html
• http://web.ukonline.co.uk/polyhedra/uniform/tocid.htm
  • A Schwarz triangle is a spherical, Euclidean, or hyperbolic triangle that covers S^2, E^2, or H^2 a finite number of times when repeatedly reflected in its sides. (Finite?!?!)

Tom Ruen 02:01, 1 February 2006 (UTC)

Cool, KaleidoTile is nice. A plan in waiting is to draw a spherical tesalation for the cubeoctahedral family illustrating the how the different polyhedra arise. --Salix alba (talk) 03:23, 1 February 2006 (UTC)

[edit] Multiple list of uniform polyhedra versions

I've been getting requests to allow versions of the list of uniform polyhedra to exist with rows sorted by different columns. (Standard approach of clickable headers which change versions should work.)

Your database approach will be great value to doing this well since values won't need duplicating. Previously I actually was contemplating writing a wikitable parser and resorting and outputing varied ordered version.

Also notice - I recently added a column for Bowers' names in the above list article.

I also just noticed the Wenninger list article has a symmetry group column which were absent from list of uniform polyhedra.

Ideally your database should include both of these columns.

Tom Ruen 02:02, 2 February 2006 (UTC)

Contents 1 Documentation 1.1 Purpose 1.2 Usage 1.2.1 Display templates 1.2.2 Short names of Polyhedron 1.2.3 Properties defined 1.3 Example 1.4 Full list of names available 1.5 How it works 1.6 See also 1.7 History 2 Discussion 2.1 Template:Infobox Polyhedron with vertfig 2.2 Multiple list of uniform polyhedra versions 2.3 Tom's test 2.4 New database 2.5 Capitalization

[edit] Tom's test

I finally made a test "full table" at: (Because I wanted the C indices!) User:Tomruen/List_of_uniform_polyhedra_and_tilings

Works very nicely!

I noticed about 12 or so polyhedral entries are apparently missing/misplaced?

Missing 12 of C(15-92): [C33, C34, C35], C41, C49, C58, C73, C76, C80, C90, C91, C92

Or 9 of U(1-75): U40, U46, U57, U60, U64, U69, U72, U74, U75

Tom Ruen 04:54, 3 March 2006 (UTC)

I filled the remaining stub articles with a "stat table" template, except for missing entries above.

Also converted all images to the png versions. I imagine if we want to consider "both", we might add a new image entry "-trimage" for "transparent image" or something, and it can be equal to "-image" if there's no other image available.

We need a few more columns as well, before older stat tables can be converted - "Dual", "Property", "Schläfli", and maybe "Type".

P.S. There are numerous failures of the vertex figure data - missing reverse orientation notations! (3/2 = retro 3), etc! Tom Ruen 10:59, 3 March 2006 (UTC)

I guess these are the snub polyhedra, I put them in a seperate template-database Template:Polyhedra snub DB, mainly for rasons of size, the snub ones are named using the Bowers notaion. Snub polyhedron should be a good example of their use. --Salix alba (talk) 20:47, 3 March 2006 (UTC)

Is there a good reason to keep them seperate? Mainly I don't want to have to guess where they are, or if I use search&replace operations for building tables.

If there is a good reason, THEN there should be a systematic code in the names which implies the DB. I mean like maybe prefix all object names? Something that can use a S&R op from names alone to generate the database and template desired.

One UNKNOWN, is my table seems slow to generate, surely from fancy template macro expansions. I have no idea if it's more efficient for one big database or a number of smaller ones, although could be tested!

Tom Ruen 21:53, 3 March 2006 (UTC)

[edit] New database

I've connected a replacement database, expanded, still in progress, work linked for now under a user page User:Tomruen/polyhedron db testing Tom Ruen 11:33, 30 December 2006 (UTC)

[edit] Capitalization

A nitpick: when using e.g. {{Uniform polyhedra db|Polyhedra word description|gdID}}, one gets text beginning "The Great ditrigonal icosidodecahedron has 20 vertices, 60 edges..."

In this context the polyhedron's name shouldn't be capitalized. It should read "The great ditrigonal icosidodecahedron has 20 vertices, 60 edges..." -- Rsholmes 19:58, 9 January 2007 (UTC)

I don't know how this could be fixed, except making two copies of every name, which isn't 100% unreasonable, just a bit of work. One of these days soon I'm going write a little parsers to convert between this format and a tab-delimited one where I can edit/create more systematically. I'll add a lower-case name then if no other solution. Tom Ruen 20:00, 9 January 2007 (UTC)