Polytope Wiki:Style guide

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This page will tell you how to format pages, page titles, etc. Anything not following this style guide should be adapted to conform to it.

If you want to make a change to this style guide, please achieve a consensus with the community first, by bringing your point up on the Discord server or the Hi.gher. Space forum.

Which polytopes get articles[edit source]

To decide which polytopes get their own articles, and which are relegated to subsections of other polytopes, the following master rule is used:

Two polytopes have separate pages if and only if they're in different teepees.
A teepee is a set of polytopes that can be continuously morphed into one another, without losing symmetry or passing through degenerate cases.

If two polytopes with different symmetries belong in the same article, the one with the highest symmetry, or highest notability, earns the title, as well as the main section and the infobox. Notability is determined by the following list:

Regular > Uniform > Uniform dual > Scaliform > CRF > Semi-uniform > Noble > Isogonal > Isotopic

For example,

get their own articles, as their symmetries are different, and their geometry is (in general) distinct. Likewise,

get their own articles: even though they have the same symmetry and can be morphed into one another, they can't be morphed without losing that symmetry or degenerating into a point.

However, there's no need for two articles

as they're in the same teepee.

Page titles[edit source]

The title for the page of a polytope must be the Bowers long name of the polytope in question. In case this doesn't exist, the Johnson name is preferred. In the cases where neither exists, the community will decide on a name.

The first word in a page title must be capitalized, but every other word must not. For example,

  • Facetorectified pentachoron Green tickY

is acceptable, but

  • Facetorectified Pentachoron Red XN
  • Firp Red XN
  • Faceted rectipyrochoron Red XN

are not. That said, redirects should be created from any alternate names, and be tagged with the corresponding redirect template.

Specific terms for high rank elements[edit source]

Specific terms for elements beyond the rank of 4, such as teron, peton, exon, zetton, yotton, etc. are generally unfamiliar to general users and do not have any inferable meaning. These terms, and their derivatives, should not be used when it is reasonably possible to avoid them in favor of more rank neutral terms.

  • Beyond rank 4 refer to polytopes of a specific rank as "n -polytopes" rather than "poly" + the facet name.
  • Similarly, beyond rank 4, use "n -simplex" and "n -orthoplex" rather than terms like "enneazetton" or "chiliaicositetraxennon".
  • To replace element names use the terms "facet", "ridge", and "peak" if applicable. If none of these is correct use the specific term or the generic "n -element".
  • Do the same for types of transitivity. Instead of an "isopetic polypeton" use the terms "facet-transitive 6-polytope" or "isotopic 6-polytope".

Permissible use of these terms are:

  • Terms may mention be mentioned to discuss the term itself. For example an article about a polytope should mention alternative names of the polytope.
  • Redirects may be made from names using these terms.
  • Terms using this language may be used when there is no established alternative.

Writing this way makes it easier to understand articles by requiring the reader to know fewer terms, and brings the wiki closer to the way professional mathematics is generally written.

Example[edit source]

The following text makes use of a number of terms which should be replaced:

The pentacosidodecayotton (also called the 9-orthoplex) is a regular polyyotton. It has 512 regular enneazetta as yotta, joining 4 to a zetton.

It can be rewritten to meet the standards of the wiki as follows:

The 9-orthoplex (also called the pentacosidodecayotton) is a regular 9-polytope. It has 512 regular 8-simplices as facets, joining 4 to a peak.

Page formatting[edit source]

A polytope's page must start by introducing the polytope by its long name. In the same sentence, common names for the polytope can be specified. The sentence must end by stating into which category the polytope falls. The next sentence must specify the facet count and vertex figure. For example,

is a valid introduction, while

  • Girco is often called the truncated cuboctahedron, but this is incorrect for various reasons. Red XN

is not.

Further information for the highest symmetry version of the polytope may be given in the introductory paragraphs. Subsections can be dedicated to describing related polytopes, notable lower symmetry versions or specific properties of any version of the polytope, with the appropriate cross-links.

Infobox polytope[edit source]

Every polytope article should have exactly one Template:Infobox polytope. All fields of the infobox that are applicable and known should be attempted to be filled. Specific guidelines apply to some of those fields:

Type[edit source]

When writing in the type of a polytope, use whichever is ranked higher in the list given in § Which polytopes get articles.

Bowers style acronyms[edit source]

Bowers style acronyms must be from either Jonathan Bowers' website or Richard Klitzing's website. Don't try and make your own without community consensus.

Elements[edit source]

Element names must be specified unless they are vertices or dyads. Element counts are grouped by symmetry; e.g. a small rhombicuboctahedron contains two groups of 6 and 12 squares in two different orbits of the symmetry group, so one may concisely state that it contains 6+12 squares.

Measures[edit source]

If applicable, measures are to be given for edge length 1. If the expressions for the measures are too long to fit in the infobox in a readable manner, approximations may instead be given, with the exact expressions being given in a Measures section. Don't fill out any fields for any measure you don't have.

If all applicable fields have been added to a polytope's infobox, but the article remains categorized in Polytopes with missing measures, add the suppress_missing_measures or the smo field and set it to "Yes". This will override this categorization. Do not override this categorization if there are any fields that can still be calculated and added.

OFF files[edit source]

Articles on polytopes that are unique up to symmetry and scaling should have their own OFF files. OFF files represent the coordinates of the vertices of a polytope, along with its combinatorial structure. For more information on the file format, see the Stella 4D manual.

OFF files are most useful for use with the Stella software, or with the Miratope software. Keep in mind that, even though Stella allows exporting 3D OFF files, uploading OFF files from Stella to the wiki is prohibited by Stella's license agreement. Make sure that every OFF file you upload to the wiki is either your own work or has been released elsewhere under an appropriate license.

Images[edit source]

The infobox should have an image of the polytope. If the polytope is 2-dimensional or less, an SVG image is preferred, though this is not enforced. For 3 and 4-dimensional polytopes, Stella images should be used if applicable. For higher-dimensional polytopes, symmetrically projected wireframes or other simpler representations suffice. In all cases, a transparent background is preferred to a white or gray background, as these clash with the infobox's background.

Stella renders should have all visible facets at their maximum size. Preferably, the visible facets should be a symmetric subset. Spheres and cylinders should be used, though the exact sizes are up to taste. The background should be made transparent; although Stella does not support doing this inside the program, external tools like Lunapic or GIMP can be used to edit the image appropriately.

Since Stella is paid software, it's understandable that not all users will be able to contribute images. To request that a specific image be added to an article, you may ask on the Discord server. Keep in mind, however, that adding images can take quite some time!

Truncation infoboxes[edit source]

Pages for Wythoffian polytopes should also use a template listing all of their truncations, like Template:o5o3o truncations. These should be generated by using Template:Truncbox, see there for further documentation.

The order in which truncates are listed should be by ring count, and then lexicographically, with ringed nodes going before unringed nodes. Any snubs should be very last. So for instance, the truncates of would go in order

,  ,  ,  ,  ,  ,  ,