Some statistics: Version 51

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1  Introduction

This page gives some statistics concerning this release of the tiling system, having 2857 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)290
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)11
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)142
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 261
Can be coloured with two colours 845
Can be coloured with two colours (straight cross-overs) 1299
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 775 1912
regular pentagon 261 3292
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 72.0 109 1049
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 1 1
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 90.0 579 1467
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 72.0 139 248
10 85.5 1 1
10 90.0 2 2
10 98.0 1 1
10 108.0 96 293
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
36.00 284
45.00 665
60.00 210
90.00 259
120.00 17

7  Does the pattern satisfy the two polygon condition?

Property Number
False 2651
True 184

8  The interlace condition

Finite interlaces Infinite interlaces Total
-1 0 64
0 0 1479
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 69
3 1 22
3 2 5
4 0 25
4 1 19
4 2 11
4 3 2
4 4 1
5 0 18
5 1 11
5 2 2
5 3 1
5 9 1
6 0 9
6 1 7
7 0 9
7 1 2
7 4 1
8 0 5
8 1 1
8 2 2
9 0 3
10 1 1
12 0 1
12 2 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 0 247
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 0 317
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 0 156
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 87
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 40
9 0 2 1
9 1 0 13
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
hill 51
aslanapa 25
wadei 674
ogel 4
erdmann 14
pc 721
paccard 92
necipoglu 28
cromwell1 1
cromwell4 30
wahhab 36
betsch 1
ww 179
broug2 59
bonner 241
cromwell2 2
hirsch 2
klaassen 1
pope 23
iran 172
smith2 98
bourgoin 179
okane2 45
bain 5
jones 49
schatt1 2
racinet 18
backhouse 7
wade 58
field2 14
pajares 25
grafton 28
balmelle 185
hessemer 55
vami 143
golomb1 29
d-avennes 41
cahier 66
rempel 21
field1 10
dawes 173
field4 26
etting 4
james 4
castera 47
fernandez 16
gands 114
abas 176
wich2 122
neal 7
dye 122
stevens 23
sarre 12
bour0 7
calvert 16
elsaid 49
broug 14
degeorge2 48
creswell 16
shafai 72
humbert 5
akber 17
murphy 5
hill2 10
briggs 12
smith1 1
critchlow 24
stronge 20
wilson 13
seherr 17
wilkinson 4
collin 38
useinov 3
grube 1
dury 3
bulut 24
lings 1
hankin2 1
booth 8
gands2 2
lee 14
gink 4
herzfeld1 1
denny 2
clevenot 14
scerrato 6
sourdel 3
dussaud 1
blair 3
rice 1
carey 5
escher 2
singer 8
rigby1 55
stierlin 3
ajlouni 1
cromwell3 1
orton 1
makov 4
martin 1
golomb2 3
reid 4
stock 6
myers 47
myers2 43
ransome 2
elsaid2 4
hedgecoe 1
herzfeld2 3
pavon 10
landau 2
burckhardt 6
schneider 1
hattstein 3
wilber 4
gluck 1
calvert2 1
jones2 1
hrbas 3
gailiunas 9
pope2 1
wich3 2
klarner 3
copple 1
volwah 2
glassner 1
marshall 17
frettloeh 18
orazi 5
rogers 2
migeon 2
muller 1
meinecke 1
berchem 1
guy 9
bakirer 1
hankin1 2
ex1995 7
betts 1
ray 13
viollet 1
hutt 2
sutton 7
otto 1
wurfel 1
gomez 1
williams 1
barry 2
stierlin2 1
siculo 1
lowry 1
arik 1
golombek 1
maussion 1
pickett 1
reuther 1
mols 1
knobloch 1
ekhtiar 1
sakkal 26
sakkal2 22
wild 1
pugatch 2
okane 1
herzfeld3 1
volait 7
blair2 1
burckhard2 1
marcais 1
herzfeld4 1
day 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 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
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