Classes of similar tilings

Many tiings have some similarities which cannot be easily found. Here there is list of such classes which have been produced to simplify find related tilings when one is located. When a tiling is found, the class is given so that related ones can be displayed. The classes are listed below with the number in each. Click on the number to list the members of that class.

Escher's Alhambra tiling pattern(6)

This pattern is unusual since the angles ensure that all the sides are in the same ratio. The angles are already determined by the regularity of the stars. This class lists a number of small variants from the one that Escher draw while at the Alhambra. They are all from Morocco or Spain (except the last which is a modern copy).

Large stars(37)

The class is those tilings with a star polygon with more than 18 points. Tiling with more than about 36 points are difficult to define adequately in a precise mathematical form used for the high-quality graphics available here.

Patterns with variants(5)

Some patterns have small variations which are handled by grouping these together with the main variant linked to the others in the group. This is the list of main variants.

Stars with 16 points with vertex angle not equal to 45°(19)

Very many 16-point stars have an angle of 45°, such as in Escher's Alhambra tiling pattern (see above). The other 16-point stars are listed here.

Regular polygons with more than eight sides(25)

The majority of these tilings are regular tiling whose enumeration has been completed. Only a few are of Islamic origin.

Tiling whose tile angles are a multiple of 45° and whose lengths are p+q*sqrt(2).(131)

These tile shapes are common in Morocco.

Tiling with three or more proper stars(58)

By proper stars, we mean excluding diamonds in the count of the number of stars. Most are Islamic with a few mathematical ones.

In Islamic Style(21)

Patterns in Islamic style which are modern inventions.

Two-level patterns(29)

These patterns first appeared in [wich2] but have been extended substantially.

Tiling with chelates(17)

This set provides a small number of related tilings.

Two-uniform tilings with regular polygons and star polygons(44)

This list is from [myers2].

Monohedral tilings with symmetry p4g(21)

Small set of tilings, mainly Islamic.

Tilings with coloured interlacing(14)

The colouring is ignored in the determination of the symmetry group and so most are p4m.

Tilings not constructible by straightedge and compass(63)

A regular (star) polygon is not constructible if the number of sides = 7, 9, 11, 13, 14, 18, 19, 21, 22, 23, 25, ... Hence we list them all here. The rest are almost certainly constructible. (We ignore modern inventions.)

Tilings with site logo Kunda Thalatha(7)

This shape consists of an equilateral triangle with three (non-regular) pentagons.