Some statistics: Version 43

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1  Introduction

This page gives some statistics concerning this release of the tiling system, having 2670 tilings.
Note that the numerical counts in the tables are actually hypertext links which give a single instance of a pattern having that characteristic.
The statistics are presented in the same order as the comprehensive search HTML form.

2  Symmetry group

The tiling has no symmetry group and hence is not a repeat pattern90
The symmetry group of the tiling is *X (cm)11
The symmetry group of the tiling is 2*22 (cmm)266
The symmetry group of the tiling is O (p1)7
The symmetry group of the tiling is 2222 (p2)34
The symmetry group of the tiling is 333 (p3)9
The symmetry group of the tiling is 3*3 (p31m)36
The symmetry group of the tiling is *333 (p3m1)20
The symmetry group of the tiling is 442 (p4)124
The symmetry group of the tiling is 4*2 (p4g)138
The symmetry group of the tiling is *442 (p4m)973
The symmetry group of the tiling is 632 (p6)92
The symmetry group of the tiling is *632 (p6m)486
The symmetry group of the tiling is XX (pg)17
The symmetry group of the tiling is 22X (pgg)17
The symmetry group of the tiling is ** (pm)20
The symmetry group of the tiling is 22* (pmg)26
The symmetry group of the tiling is *2222 (pmm)164
The symmetry group of the tiling is *22∞ (pma2)4
The symmetry group of the tiling is 2*∞ (pmm2)1
The symmetry group of the tiling is *2• (d2)3
The symmetry group of the tiling is 2• (c2)30
The symmetry group of the tiling is 3• (c3)22
The symmetry group of the tiling is *4• (d4)13
The symmetry group of the tiling is 4• (c4)8
The symmetry group of the tiling is *5• (d5)9
The symmetry group of the tiling is 5• (c5)4
The symmetry group of the tiling is *6• (d6)4
The symmetry group of the tiling is 6• (c6)14
The symmetry group of the tiling is 7• (c7)1
The symmetry group of the tiling is *8• (d8)15
The symmetry group of the tiling is *10• (d10)9
The symmetry group of the tiling is *12• (d12)2
The symmetry group of the tiling is 12• (c12)1
Note how unevenly the groups appear. Given a tiling of a `rare' group, it would then be easy to examine each tiling by eye for a match.

3  Two colour property

Property Number
Colouring could not be determined 243
Cannot be coloured with two colours 814
Can be coloured with two colours 424
Can be coloured with two colours (straight cross-overs) 1189
Most of the cases in which the colouring could not be determined is due to the software not being capable enough.

4  Tilings containing regular polygons

Polygon Number of TilingsTotal
equilateral triangle 240 709
square 723 1826
regular pentagon 241 3204
regular hexagon 307 483
regular heptagon 24 84
regular octagon 196 266
regular enneagon 6 6
regular decagon 6 10
12-gon 10 10
16-gon 2 2
18-gon 1 1
24-gon 1 1

5  Tilings containing regular star polygons

Points Vertex angle Tiling count Total
2 (undef) 1 10
2 0.0 2 2
2 15.0 1 1
2 18.0 4 6
2 22.5 3 4
2 25.7 12 32
2 30.0 22 41
2 34.3 1 1
2 36.0 10 16
2 45.0 184 1053
2 48.0 1 1
2 50.0 2 2
2 51.4 4 8
2 52.5 1 2
2 53.1 1 1
2 58.5 1 1
2 60.0 167 284
2 63.0 1 1
2 66.0 1 1
2 67.5 2 8
2 70.0 2 2
2 70.7 1 8
2 72.0 96 1100
2 73.1 2 16
2 75.0 4 7
2 77.1 9 21
2 78.0 2 3
2 80.0 5 7
2 82.5 1 1
2 90.0 2 2
2 92.6 1 1
2 100.0 1 1
2 105.0 1 1
2 108.0 2 30
2 117.0 1 1
2 120.0 2 2
2 135.0 7 26
3 15.0 7 8
3 18.0 4 4
3 20.0 2 2
3 22.0 3 4
3 25.7 1 1
3 30.0 27 34
3 34.3 5 6
3 37.5 1 1
3 40.0 3 3
3 45.0 4 4
3 60.0 9 9
3 80.0 1 1
3 90.0 27 43
3 100.0 2 2
3 102.0 1 1
3 105.0 6 6
3 108.0 1 1
3 112.5 3 3
3 120.0 1 1
3 135.0 2 2
3 150.0 3 3
3 165.0 1 1
4 0.0 1 1
4 18.0 2 3
4 22.0 2 3
4 24.0 1 1
4 30.0 11 13
4 31.5 1 1
4 36.0 1 1
4 45.0 81 115
4 48.0 1 1
4 51.4 1 3
4 52.5 1 1
4 54.0 4 4
4 56.3 1 1
4 60.0 37 39
4 63.0 1 1
4 64.3 5 6
4 65.0 1 1
4 67.5 8 8
4 68.0 1 1
4 70.0 2 2
4 75.0 3 3
4 90.0 4 4
4 120.0 24 28
4 126.0 3 3
4 135.0 10 10
4 150.0 2 2
5 36.0 53 347
5 48.0 1 1
5 72.0 19 65
5 108.0 2 2
6 0.0 1 1
6 15.0 1 1
6 18.0 1 1
6 20.0 1 1
6 22.0 1 3
6 30.0 18 19
6 36.0 1 1
6 40.0 2 2
6 45.0 1 1
6 48.0 3 3
6 60.0 217 247
6 65.0 1 1
6 72.0 7 7
6 73.3 1 1
6 75.0 8 8
6 76.0 1 1
6 77.1 1 1
6 78.0 2 2
6 78.8 1 1
6 80.0 4 4
6 84.0 1 1
6 85.0 3 3
6 90.0 46 47
6 94.3 4 4
6 95.0 1 1
6 100.0 2 2
6 102.9 1 1
6 105.0 2 2
6 108.0 2 2
6 114.0 1 1
6 120.0 15 15
6 135.0 1 1
6 150.0 3 3
7 0.0 7 7
7 77.1 11 12
7 92.6 1 2
7 102.9 1 1
8 0.0 10 10
8 15.0 9 10
8 18.0 1 1
8 25.0 1 1
8 45.0 133 265
8 50.0 1 1
8 52.5 1 1
8 55.0 1 1
8 60.0 2 2
8 65.0 2 2
8 67.5 4 5
8 69.0 1 1
8 70.0 3 3
8 71.3 3 3
8 72.0 6 7
8 73.1 3 3
8 75.0 6 6
8 76.5 1 1
8 80.0 2 2
8 90.0 540 1447
8 100.0 2 4
8 105.0 6 6
8 108.0 2 2
8 109.3 1 1
8 111.0 1 1
8 112.5 8 8
8 115.0 1 1
8 117.0 1 1
8 120.0 4 4
8 121.5 1 1
8 135.0 3 3
9 0.0 5 5
9 20.0 3 3
9 30.0 1 1
9 32.0 1 1
9 40.0 5 5
9 70.0 3 3
9 72.0 1 1
9 72.5 2 2
9 80.0 11 11
9 92.0 1 1
9 100.0 2 2
9 105.0 1 1
9 110.0 3 3
9 120.0 1 1
10 0.0 2 2
10 36.0 3 3
10 54.0 1 1
10 72.0 120 206
10 85.5 1 1
10 90.0 2 2
10 98.0 1 1
10 108.0 88 284
10 126.0 1 1
11 0.0 3 3
12 0.0 7 7
12 15.0 1 1
12 30.0 18 18
12 45.0 1 1
12 51.0 1 1
12 52.5 3 3
12 60.0 141 176
12 65.0 2 2
12 66.0 2 2
12 67.5 1 1
12 70.0 4 4
12 71.3 2 2
12 72.0 8 8
12 72.5 2 2
12 75.0 12 12
12 78.0 1 1
12 80.0 4 4
12 82.5 1 1
12 84.0 1 1
12 85.0 1 1
12 90.0 49 50
12 97.5 4 4
12 100.0 3 3
12 105.0 8 8
12 120.0 7 7
12 124.3 1 1
12 127.5 1 1
13 0.0 1 1
14 51.4 8 8
14 70.7 3 3
14 77.1 3 3
14 102.9 16 19
15 51.0 1 1
16 0.0 3 3
16 22.5 1 1
16 45.0 82 84
16 52.5 3 3
16 58.5 1 1
16 59.0 1 1
16 60.0 2 2
16 62.5 1 1
16 67.5 4 4
16 73.1 3 3
16 75.0 1 1
16 80.0 1 1
16 90.0 5 5
16 100.0 1 1
18 40.0 2 2
18 44.0 1 1
18 60.0 2 2
18 80.0 4 4
20 0.0 1 1
20 36.0 6 6
20 54.0 1 1
20 60.0 1 1
24 0.0 5 5
24 30.0 13 13
24 40.0 1 1
24 45.0 3 3
32 0.0 1 1
32 22.5 1 1
48 0.0 4 4

6  The angles of the tiling

Angle Number
- 90
0.38 1
0.50 4
1.00 6
1.07 1
1.25 8
1.50 7
1.67 1
1.88 3
2.00 11
2.14 1
2.50 22
2.81 3
3.00 9
3.21 4
3.75 15
4.29 4
4.50 7
5.00 38
5.63 1
6.00 14
6.43 1
7.50 87
8.57 4
9.00 14
10.00 13
11.25 21
12.00 11
12.86 6
15.00 235
18.00 34
20.00 16
22.50 259
25.71 30
30.00 325
36.00 249
45.00 644
60.00 199
90.00 255
120.00 17

7  Does the pattern satisfy the two polygon condition?

Property Number
False 2468
True 185

8  The interlace condition

Finite interlaces Infinite interlaces Total
-1 0 72
0 0 1406
0 1 227
0 2 168
0 3 36
0 4 21
0 5 3
0 6 1
0 8 1
1 0 127
1 1 136
1 2 53
1 3 5
1 4 1
1 5 3
1 7 1
2 0 109
2 1 67
2 2 16
2 3 8
2 4 1
2 5 1
3 0 51
3 1 20
3 2 5
3 3 15
4 0 24
4 1 14
4 2 5
4 3 2
4 4 1
5 0 17
5 1 10
5 2 2
6 0 9
6 1 7
7 0 9
7 1 2
7 4 1
8 0 4
8 2 2
9 0 3
10 1 1
12 0 1
13 0 1
15 3 1

9  Polygonal tiles used

This excludes the regular polygons and star polygons.
Reflective tilesReflective pairs No mirror image Number
0 0 0 236
0 0 1 141
0 0 2 56
0 0 3 10
0 0 4 2
0 0 6 1
0 0 7 2
0 0 8 35
0 0 9 2
0 0 11 2
0 1 0 90
1 0 0 421
1 0 1 23
1 0 2 6
1 0 4 2
1 1 0 33
1 2 0 2
1 3 0 3
2 0 0 256
2 0 1 5
2 0 2 3
2 0 3 1
2 0 6 1
2 1 0 25
2 1 1 1
2 2 0 4
2 3 0 1
2 4 0 2
2 5 0 2
2 6 0 1
3 0 0 298
3 0 1 1
3 0 2 4
3 0 5 2
3 1 0 27
3 2 0 3
3 2 2 1
3 3 0 2
3 4 0 1
3 5 0 2
4 0 0 182
4 0 2 1
4 0 5 2
4 1 0 17
4 2 0 6
4 3 0 2
4 6 0 1
5 0 0 146
5 0 2 1
5 1 0 22
5 2 0 2
5 3 0 2
6 0 0 90
6 1 0 25
6 2 0 4
6 4 0 1
7 0 0 73
7 0 2 3
7 1 0 18
7 2 0 3
7 3 0 1
7 4 0 1
8 0 0 54
8 1 0 14
8 2 0 6
8 3 0 3
9 0 0 37
9 0 2 1
9 1 0 13
9 2 0 3
9 4 2 1
10 0 0 32
10 1 0 7
10 2 0 5
10 4 0 2
11 0 0 17
11 1 0 9
11 2 0 3
12 0 0 23
12 1 0 9
12 2 0 5
12 3 0 1
12 4 0 1
13 0 0 8
13 0 2 1
13 1 0 3
13 2 0 6
13 3 0 1
13 4 0 1
14 0 0 8
14 1 0 5
14 1 6 1
14 2 0 7
15 0 0 3
15 1 0 7
15 2 0 5
16 0 0 5
16 1 0 4
16 2 0 3
16 3 0 1
17 0 0 4
17 1 0 1
17 2 0 3
17 3 0 4
18 0 0 5
18 1 0 4
18 3 0 1
18 8 0 1
19 1 0 3
19 2 0 2
20 1 0 1
20 3 0 1
21 0 13 1
21 1 0 1
21 2 0 1
22 4 0 1
22 5 0 1
23 0 0 1
23 1 0 1
23 4 0 2
24 7 0 1
26 4 0 1
26 5 0 1

10  Edge-to-edge property

Property Number
False 580
True 2074

11  Publications

Publication Number
abas 177
akber 18
arik 1
aslanapa 25
backhouse 7
bain 5
bakirer 1
balmelle 186
barry 2
berchem 1
betsch 1
betts 1
blair 3
booth 8
bour0 7
bourgoin 177
briggs 12
broug 15
broug2 59
burckhardt 6
cahier 66
calvert 16
calvert2 1
carey 5
castera 46
clevenot 14
collin 35
copple 1
creswell 16
critchlow 24
cromwell1 1
cromwell2 2
cromwell3 1
d-avennes 41
dawes 174
degeorge2 47
denny 2
dury 3
dussaud 1
dye 122
ekhtiar 1
elsaid 49
elsaid2 4
erdmann 2
escher 2
ex1995 7
fernandez 14
field1 10
field2 14
field4 26
frettloeh 19
gailiunas 8
gands 114
gands2 2
gink 4
glassner 1
gluck 1
golomb1 29
golomb2 3
golombek 1
gomez 1
grafton 28
grube 1
guy 9
hankin1 2
hankin2 1
hattstein 3
hedgecoe 1
herzfeld1 1
herzfeld2 3
herzfeld3 1
hessemer 55
hill 45
hill2 10
hrbas 3
humbert 5
hutt 2
iran 170
james 4
jones 50
jones2 1
klarner 3
knobloch 1
landau 2
lee 14
lings 1
lowry 1
makov 4
marshall 17
martin 1
maussion 1
meinecke 1
migeon 2
mols 1
muller 1
murphy 5
myers 47
myers2 43
neal 7
necipoglu 26
ogel 4
okane 1
okane2 45
orazi 4
orton 1
otto 1
paccard 92
pajares 25
pavon 10
pc 641
pickett 1
pope 23
pope2 1
pugatch 2
racinet 18
ransome 2
ray 13
reid 4
rempel 20
reuther 1
rice 1
rigby1 55
rogers 2
sakkal 25
sarre 12
scerrato 6
schatt1 2
seherr 17
shafai 73
siculo 1
singer 8
smith1 1
smith2 97
sourdel 3
stevens 23
stierlin 3
stierlin2 1
stock 6
stronge 20
sutton 7
useinov 3
vami 50
viollet 1
volait 7
volwah 2
wade 59
wadei 652
wahhab 36
wich2 122
wich3 2
wilber 4
wild 11
wilkinson 4
williams 1
wilson 13
wurfel 1

12  Islamic Tilings

Those tilings which are referenced at least once in books about Islamic art can be counted as Islamic patterns. There are 1488 of these.

13  Photographic links

There are 718 tiling patterns whose records link to a photograph. The total number of links to photographs is 1024.

14  Version records

Version Date TilingsComment
43 2017-09-10 2670See.
42 2016-09-27 2620See.
41 2016-05-14 2603See.
40 2016-02-01 2566See.
39 2015-11-28 2548See.
38 2015-09-04 2527See.
37 2015-04-20 2517See.
36 2014-11-29 2510See.
35 2014-08-03 2505See.
34 2014-06-06 2429See.
33 2014-03-08 2440See.
32 2013-12-11 2389See.
31 2013-10-08 2336More patterns from Iran
30 2013-08-08 2304All patterns have a PDF version
29 2013-05-01 2304Patterns from Nick Crossling added
28 2013-02-19 2278Patterns from Alberto Leon added
27 2012-12-16 2235Patterns in Islamic style added from Tony Lee
26 2012-10-16 2201More Roman mosaic patterns added
25 2012-08-21 2151Roman mosaic patterns added
24 2012-05-28 2020More paterns from the Alhambra added
23 2012-02-11 1983More pattern added from David Wade's photos
22 2011-12-17 1941More patterns from Borgoin added
21 2011-09-19 1908Patterns with borders added
20 2011-06-21 1868Example of internal documentation provided
19 2011-02-28 182925 patterns from Tony Lee
18 2010-11-15 1771More paterns from the Alhambra added
17 2010-08-14 1727Large JPG display added for some patterns
16 2010-05-07 1695Some V and A material added
15 2010-01-29 1646Entry page display added
14 2009-12-09 1601Tilings of a square with similar triangles added
13 2009-10-09 1563Two-uniform tilings added
12 2009-06-20 1499Patterns from Borgoin added
11 2009-03-05 1442Patterns on the Alhambra added
10 2009-01-03 1403Random display of 20 patterns added
9 2008-11-16 1353Limks to David Wade's photos added
8 2008-09-29 1319Polyominoes tilings added
7 2008-06-22 1190Tree search and Conway-Thurston notation
6 2008-05-05 1178Tilings from Stevens
5 2008-03-31 1153Islamic tilings from DeGeorge
4 2008-02-23 1130Spiral tilings added
3 2007-12-27 1106Further Islamic tilings added
2 2007-11-05 1085First version on Internet
1 2007-10-06 1076Islamic tiling added
0 2007-08-26 1050Initial system