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(7)
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(43)
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(6)
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°(31)
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(31)
The majority of these tiling are regular tiling whose enumeration has been completed.
Only three are of Islamic origin.
Tiling whose tile angles are a multiple of 45° and whose lengths are p+q√2.(161)
These tile shapes are common in Morocco.
Tiling with three or more proper stars(70)
By proper stars, we mean excluding diamonds in the count of the number of stars.
There are four mathematical ones, and the rest are Islamic.
The last two patterns are alternative representation of the same artifact for
which a photograph is available. One has straight interlacing, but the original
has kinks in two places which is faithfully copied in the other alternative.
In Islamic Style(22)
Patterns in Islamic style which are modern inventions.
Two-level patterns(35)
These patterns first appeared in [wich2] but have been extended substantially.
Tilings with Chelates(19)
This set provides a small number of related tilings.
Two-uniform tilings with regular polygons and star polygons(44)
This list is from Joseph Myers, see.
Monohedral tilings with symmetry group p4g(24)
Small set of tilings, mainly Islamic.
Tilings with coloured interlacing(18)
This is new to version 17 and required an enhancement to the software used
to construct the graphics. The interlacing is not ignored in
computing the symmetry group.
Tilings which are not constructible with straightedge and compass(99)
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.
Tilings with site logo Kunda Thalatha(17)
This shape consists of an equilateral triangle with three (non-regular) pentagons.
Tilings from copies of a Koran(31)
These patterns are not geometrically related, but provides an interesting set.
Square Kufic tessellations(24)
Tessellations where words are written in Square Kufic and their shape manipulated in such a way to make the space or background area between the letters also read as text. One historical example is where the name Ali is repeated three times in black in the foreground and three times in white in the background. Other examples include the name Ali repeated two times each in the foreground and background, and the names Muhammad and Ali repeated four times, one name in the foreground and the other in the background.
First Decagonal motif(18)
This motif consists of three type tiles with 11 in total in a d5 arrangement.
Second Decagonal motif(3)
This motif consists of four type tiles with 21 in total in a d5 arrangement.
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