Category:Templates to categorize mathematical objects by size

Most of these template take one argument, and just pass it on. E.g. {{Cayley tables by order|8}} in Cayley tables of order 8 produces:

[[Category:Cayley tables by order| 00008]]
[[Category:Groups of order 8]]
[[Category:8×8 matrices]]

Some make operations like addition, e.g. {{Star graphs by size|5}} in Star graph S5 produces:

[[Category:Star graphs by size| 00005]]
[[Category:Graphs with 6 vertices]]

Some take two arguments, e.g. Template:MatrixCat and Template:Duoprisms by size. Both calculate the product of the arguments, and check if they are equal.

Some map numbers to words, e.g. {{PolygonCat|13}} will output [[Category:Tridecagons]].

Sometimes switch has to be used to catch special cases. E.g. Regular pentagons is not directly in Pentagons, but via Equilateral pentagons and Equiangular pentagons. The code in Template:Regular polygons by size looks like this:

{{#switch: {{{1}}}
| 5 = [[Category:Equilateral pentagons]][[Category:Equiangular pentagons]]
| {{PolygonCat|{{{1}}}}}
}}

The same templates sorts into angle categories if the angle is an integer:

{{#switch: {{mod|360|{{{1}}}}}
| 0 = [[Category:{{#expr:360/{{{1}}}}}°]][[Category:{{#expr:180-360/{{{1}}}}}°]]
}}

Actually there is another switch within that, because 90° is at Right angles:

{{#switch: {{mod|360|{{{1}}}}}
| 0 = {{#switch: {{#expr:180-360/{{{1}}}}} | 90 = [[Category:Right angles]] | [[Category:{{#expr:360/{{{1}}}}}°]][[Category:{{#expr:180-360/{{{1}}}}}°]]}}
}}

There are no other groups of prime order than cyclic groups. Unfortunately there seems to be no template that checks if a number is prime. So {{Cycle graphs of cyclic groups by size}} includes this poor solution, sorting e.g. Cycle graph of C7 directly in Group cycle graphs by order:

{{#switch: {{{1}}}
| 2 = [[Category:Group cycle graphs by order| {{padleft:{{{1}}}|5}}]]
| 3 = [[Category:Group cycle graphs by order| {{padleft:{{{1}}}|5}}]]
| 5 = [[Category:Group cycle graphs by order| {{padleft:{{{1}}}|5}}]]
| 7 = [[Category:Group cycle graphs by order| {{padleft:{{{1}}}|5}}]]
| 11 = [[Category:Group cycle graphs by order| {{padleft:{{{1}}}|5}}]]
| 13 = [[Category:Group cycle graphs by order| {{padleft:{{{1}}}|5}}]]
| [[Category:Group cycle graphs of order {{{1}}}]]
}}

See also: Category:Commons utility templates, Category:Mathematical function templates