Search Tilings

Help for Tilings Search.

Empty fields match all possible targets. Restrict the search by including possible matches. Different fields are AND'd together. Multiple strings within a single field are AND'd together for Ring Size and Vertex Degree (as these sets are overlapping), but OR'd together for Orbifold and Optype (as these sets are mutually exclusive).

For example

Ring Size: 3 6
Vertex Degree: 5

will find all tilings with 3 AND 6 in the Schläfli symbol AND a 5 in the vertex Degree

Exclusive Matching

A standard match, for instance;

Vertex Degree: 3 4

Will get all vertex degrees containing both 3 AND 4 so {3,4,5} would match.

To get all tilings with only a particular vertex degree and no other, use the ONLY keyword eg.

3 4 ONLY

will match tilings with degrees {3,4} or {4,3} or {3,3,4} but never {3,4,5}}

Substring Matching

You can match more tightly than this too, in the Rings, for instance;

Ring Size: 3.4.4

will pick out all Tilings with that exact ring sequence. It doesn't handle string boundaries yet, so if the Schläfli symbol contains {4.5.3.4}, which actually does contain a ring sequence of 3.4.4, it won't detect it.

You can do tighter matches on the Vertex degree, eg;

Vertex Degree: 4,5

will match on any Vertex Degrees containing this ordered substring. To match an exact signature, use brackets, eg:

Vertex Degree: {4,5}

This is an ordered search, so it won't match on {5,4}

Ring Size: {3.3.3}

will match any Schläfli containing {3.3.3}

Negation

Ring and Vertex searching admit the Negation operator '^'. To exclude a particular ring or vertex from a match, eg,

Ring Size: 4 8 ^3

will find all matching ring sizes with 4 and 8 but not 3. This also applies to substring searching, eg.

Vertex Degrees: ^{4,5} will match everything but {4,5}

Search within a Category - Orbifold & Optype

To restrict searches to specific categories, give Orbifold or Optype strings. The menus are provided to give examples of the options, but they are only a guide - you must type the string(s) you want into the textbox. eg,

Orbifolds: *246
Operation Types: FSG

restricts to '*246' AND 'FSG'

Multiple entries within these fields are possible, and they are OR'd together (they are non-overlapping, so an AND would give you a null set)

Orbifolds: *2224 *2223
Operation Types: F FG

should find ('*2224' OR '*2223') AND ('F' OR 'FG')