Some statistics: Version 52

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1  Introduction

This page gives some statistics concerning this release of the tiling system, having 2862 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 symmetry group of the tiling is *632 (p6m)522
The symmetry group of the tiling is *8• (d8)17
The symmetry group of the tiling is *2222 (pmm)184
The symmetry group of the tiling is 2*22 (cmm)293
The symmetry group of the tiling is *442 (p4m)1025
The symmetry group of the tiling is 3*3 (p31m)35
The symmetry group of the tiling is *5• (d5)13
The symmetry group of the tiling is 6• (c6)19
The symmetry group of the tiling is *6• (d6)6
The symmetry group of the tiling is *4• (d4)16
The symmetry group of the tiling is *10• (d10)12
The symmetry group of the tiling is *12• (d12)5
The symmetry group of the tiling is 442 (p4)124
The symmetry group of the tiling is *333 (p3m1)21
The symmetry group of the tiling is 22X (pgg)17
The symmetry group of the tiling is 4*2 (p4g)143
The symmetry group of the tiling is ** (pm)21
The symmetry group of the tiling is 632 (p6)98
The symmetry group of the tiling is *X (cm)13
The symmetry group of the tiling is 22* (pmg)28
The symmetry group of the tiling is 333 (p3)9
The symmetry group of the tiling is *2• (d2)13
The symmetry group of the tiling is 4• (c4)32
The symmetry group of the tiling is 2222 (p2)34
The symmetry group of the tiling is 2• (c2)34
The symmetry group of the tiling is not symmetric and hence is not a repeat pattern82
The symmetry group of the tiling is 5• (c5)5
The symmetry group of the tiling is 3• (c3)3
The symmetry group of the tiling is XX (pg)18
The symmetry group of the tiling is O (p1)7
The symmetry group of the tiling is 7• (c7)1
The symmetry group of the tiling is 12• (c12)1
The symmetry group of the tiling is *22∞ (p2mm)6
The symmetry group of the tiling is *3• (d3)1
The symmetry group of the tiling is *16• (d16)1
The symmetry group of the tiling is 2*∞ (pmg)2
The symmetry group of the tiling is *1• (d1)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 452
Cannot be coloured with two colours 263
Can be coloured with two colours 845
Can be coloured with two colours (straight cross-overs) 1302
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 252 722
square 776 1914
regular pentagon 265 3398
regular hexagon 316 495
regular heptagon 28 87
regular octagon 220 285
regular enneagon 8 8
regular decagon 6 10
12-gon 12 12
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) 2 11
2 0.0 2 2
2 15.0 1 1
2 18.0 4 6
2 22.5 4 8
2 25.7 12 30
2 30.0 21 37
2 34.3 1 1
2 36.0 11 23
2 40.0 1 1
2 45.0 197 890
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 55.5 1 1
2 58.5 1 1
2 60.0 178 289
2 63.0 2 2
2 66.0 1 1
2 67.5 2 8
2 70.0 2 2
2 70.7 1 7
2 72.0 110 1072
2 73.1 2 16
2 75.0 8 13
2 77.1 10 18
2 78.0 2 2
2 80.0 6 7
2 82.5 1 1
2 87.4 1 1
2 99.2 1 1
3 15.0 7 8
3 18.0 4 4
3 20.0 3 3
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 36 42
3 100.0 1 1
3 102.0 1 1
3 105.0 12 12
3 108.0 1 1
3 112.5 3 3
3 120.0 1 1
3 150.0 3 4
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 13 15
4 31.5 1 1
4 36.0 1 1
4 40.0 1 1
4 45.0 81 103
4 48.0 1 1
4 51.4 1 1
4 52.5 1 1
4 54.0 5 5
4 56.3 1 1
4 60.0 42 44
4 63.0 1 1
4 64.3 5 6
4 65.0 1 1
4 67.5 7 7
4 68.0 1 1
4 70.0 2 2
4 75.0 3 3
4 90.0 4 4
4 98.0 1 1
4 120.0 28 31
4 126.0 3 3
4 135.0 10 10
5 (undef) 1 1
5 36.0 64 331
5 48.0 1 1
5 72.0 28 61
5 108.0 2 2
6 (undef) 1 1
6 0.0 2 2
6 15.0 1 1
6 18.0 1 1
6 20.0 1 1
6 22.0 1 3
6 30.0 19 20
6 36.0 1 1
6 40.0 3 3
6 45.0 2 2
6 48.0 3 3
6 60.0 230 264
6 65.0 1 1
6 72.0 7 7
6 73.3 1 1
6 75.0 9 9
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 51 51
6 94.3 4 4
6 95.0 1 1
6 100.0 3 3
6 102.9 1 1
6 105.0 3 3
6 108.0 2 2
6 114.0 1 1
6 120.0 14 14
6 135.0 1 1
6 150.0 2 2
7 (undef) 3 4
7 0.0 12 12
7 77.1 11 12
7 92.6 1 2
7 102.9 2 2
8 (undef) 2 2
8 0.0 11 11
8 15.0 9 10
8 18.0 1 1
8 25.0 1 1
8 35.0 1 1
8 45.0 159 235
8 50.0 1 1
8 52.5 1 1
8 55.0 1 1
8 60.0 2 2
8 63.0 1 1
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 8 8
8 76.5 1 1
8 80.0 2 2
8 82.0 1 1
8 90.0 580 1479
8 100.0 2 4
8 105.0 9 9
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 5 5
8 121.5 1 1
8 135.0 3 3
9 0.0 7 7
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 13 13
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 (undef) 2 2
10 0.0 3 3
10 36.0 5 5
10 54.0 1 1
10 72.0 140 250
10 85.5 1 1
10 90.0 2 2
10 98.0 1 1
10 108.0 98 309
10 126.0 1 1
11 (undef) 1 1
11 0.0 4 4
11 70.0 1 1
12 (undef) 2 2
12 0.0 10 10
12 15.0 1 1
12 30.0 20 20
12 45.0 1 1
12 51.0 1 1
12 52.5 3 3
12 60.0 151 186
12 65.0 3 3
12 66.0 2 2
12 67.5 1 1
12 70.0 5 5
12 71.3 2 2
12 72.0 8 8
12 72.5 2 2
12 75.0 15 15
12 78.0 1 1
12 80.0 8 8
12 82.5 1 1
12 84.0 1 1
12 85.0 1 1
12 90.0 55 56
12 97.5 4 4
12 100.0 2 2
12 105.0 10 10
12 120.0 8 8
12 124.3 1 1
12 127.5 1 1
13 0.0 1 1
13 90.0 1 1
14 0.0 1 1
14 51.4 8 8
14 70.7 3 3
14 77.1 4 4
14 102.9 16 19
15 51.0 2 2
16 0.0 4 4
16 22.5 1 1
16 45.0 86 88
16 52.5 4 4
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 6 6
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 (undef) 2 2
20 0.0 1 1
20 36.0 7 7
20 54.0 1 1
20 60.0 1 1
24 (undef) 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
- 103
0.38 1
0.50 7
1.00 7
1.07 1
1.25 8
1.50 8
1.67 1
1.88 3
2.00 11
2.14 1
2.50 28
2.81 3
3.00 10
3.21 4
3.75 17
4.00 1
4.29 4
4.50 11
5.00 40
5.63 1
6.00 14
6.43 2
7.50 97
8.57 4
9.00 14
10.00 14
11.25 21
12.00 11
12.86 7
15.00 259
18.00 38
20.00 20
22.50 276
25.71 34
30.00 341
36.00 288
45.00 666
60.00 210
90.00 259
120.00 17

7  Does the pattern satisfy the two polygon condition?

Property Number
False 2656
True 184

8  The interlace condition

Finite interlaces Infinite interlaces Total
-1 0 64
0 0 1480
0 1 233
0 2 173
0 3 44
0 4 22
0 5 5
0 6 3
0 8 2
1 0 135
1 1 156
1 2 55
1 3 10
1 4 1
1 5 3
1 7 1
2 0 142
2 1 71
2 2 16
2 3 9
2 4 1
2 5 1
3 0 70
3 1 23
3 2 5
4 0 25
4 1 19
4 2 11
4 3 2
4 4 1
5 0 17
5 1 11
5 2 2
5 3 1
5 9 1
6 0 10
6 1 7
7 0 9
7 1 2
7 4 1
8 0 6
8 1 1
8 2 2
9 0 3
10 1 1
12 0 1
12 2 1
13 0 1
15 3 2

9  Polygonal tiles used

This excludes the regular polygons and star polygons.
Reflective tilesReflective pairs No mirror image Number
0 0 0 247
0 0 1 153
0 0 2 57
0 0 3 11
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 95
1 0 0 419
1 0 1 21
1 0 2 1
1 0 4 2
1 0 6 1
1 1 0 49
1 2 0 2
1 3 0 3
2 0 0 285
2 0 1 5
2 0 2 3
2 0 3 1
2 0 6 1
2 1 0 26
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 0 320
3 0 1 2
3 0 2 3
3 0 5 2
3 1 0 29
3 2 0 3
3 3 0 3
3 4 0 1
3 5 0 2
4 0 0 217
4 0 5 3
4 1 0 19
4 2 0 7
4 3 0 2
4 6 0 1
5 0 0 155
5 0 2 1
5 1 0 26
5 2 0 3
5 3 0 2
6 0 0 102
6 1 0 28
6 2 0 4
6 4 0 1
7 0 0 88
7 0 2 1
7 1 0 22
7 2 0 3
7 3 0 1
7 4 0 1
8 0 0 58
8 1 0 15
8 2 0 7
8 3 0 3
9 0 0 41
9 0 2 1
9 1 0 14
9 2 0 4
9 5 0 1
10 0 0 33
10 1 0 7
10 2 0 6
10 3 0 1
10 4 0 3
11 0 0 20
11 1 0 9
11 2 0 4
12 0 0 15
12 1 0 9
12 2 0 5
12 2 2 1
12 3 0 1
12 4 0 1
13 0 0 9
13 1 0 4
13 2 0 6
13 3 0 1
13 4 0 1
14 0 0 8
14 1 0 6
14 2 0 7
14 3 2 1
15 0 0 3
15 1 0 7
15 2 0 5
15 4 0 2
16 0 0 5
16 0 22 1
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 3
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 1 0 1
21 2 0 1
22 0 13 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 0
True 601

11  Publications

Publication Number
abas 176
ajlouni 1
akber 17
arik 1
aslanapa 25
backhouse 7
bain 5
bakirer 1
balmelle 185
barry 2
berchem 1
betsch 1
betts 1
blair 3
blair2 1
bonner 241
booth 8
bour0 7
bourgoin 179
briggs 12
broug 14
broug2 59
bulut 24
burckhard2 1
burckhardt 6
cahier 66
calvert 16
calvert2 1
carey 5
castera 47
clevenot 14
collin 38
copple 1
creswell 16
critchlow 24
cromwell1 1
cromwell2 2
cromwell3 1
cromwell4 30
d-avennes 41
dawes 173
day 1
degeorge2 48
denny 2
dury 3
dussaud 1
dye 122
ekhtiar 1
elsaid 49
elsaid2 4
erdmann 14
escher 2
etting 4
ex1995 7
fernandez 16
field1 10
field2 14
field4 26
frettloeh 18
gailiunas 9
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
herzfeld4 1
hessemer 55
hill 51
hill2 10
hirsch 2
hrbas 3
humbert 5
hutt 2
iran 172
james 4
jones 50
jones2 2
klaassen 1
klarner 3
knobloch 1
landau 2
lee 14
lings 1
lowry 1
makov 4
marcais 1
marshall 17
martin 1
maussion 1
meinecke 1
migeon 2
mols 1
muller 1
murphy 5
myers 47
myers2 43
neal 7
necipoglu 28
ogel 4
okane 1
okane2 45
orazi 5
orton 1
otto 1
paccard 92
pajares 25
pavon 10
pc 739
pickett 1
pope 23
pope2 1
pugatch 2
racinet 18
ransome 2
ray 13
reid 4
rempel 21
reuther 1
rice 1
riefstahl 1
rigby1 55
rogers 2
sakkal 26
sakkal2 22
sarre 12
scerrato 6
schatt1 2
schneider 1
seherr 17
shafai 72
siculo 1
singer 8
smith1 1
smith2 98
sourdel 3
stevens 23
stierlin 3
stierlin2 1
stock 6
stronge 20
sutton 7
useinov 3
vami 143
viollet 1
volait 7
volwah 2
wade 58
wadei 674
wahhab 36
wich2 122
wich3 2
wilber 4
wild 1
wilkinson 4
williams 1
wilson 13
wurfel 1
ww 179

12  Islamic Tilings

Those tilings which are referenced at least once in books about Islamic art can be counted as Islamic patterns. There are 1663 of these.

13  Photographic links

There are 775 tiling patterns whose records link to a photograph. The total number of links to photographs is 1150.

14  Version records

Version Date TilingsComment
52 2021-08-15 2862See.
51 2020-11-23 2857See.
50 2020-08-01 2840See.
49 2019-08-01 2811See.
48 2019-03-15 2812See.
47 2018-09-29 2767See.
46 2018-07-22 2717See.
45 2018-05-15 2714See.
44 2017-12-28 2690See.
43 2017-09-10 2670See.
42 2016-09-27 2620See.
41 2016-05-14 2603See.
40 2016-02-01 2566See.
39 2015-11-28 254821 new patterns
38 2015-09-04 2527Negative searching
37 2015-04-20 2517New search facility
36 2014-11-29 2510Interlace counts
35 2014-08-03 2505James William Wild
34 2014-06-06 2429Chelates
33 2014-03-08 2440Variant patterns
32 2013-12-11 2389Kites and Darts
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