Some statistics: Version 42

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1  Introduction

This page gives some statistics concerning this release of the tiling system, having 2621 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)257
The symmetry group of the tiling is O (p1)5
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)121
The symmetry group of the tiling is 4*2 (p4g)136
The symmetry group of the tiling is *442 (p4m)952
The symmetry group of the tiling is 632 (p6)93
The symmetry group of the tiling is *632 (p6m)477
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)160
The symmetry group of the tiling is *22∞ (pma2)3
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)5
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 242
Cannot be coloured with two colours 807
Can be coloured with two colours 422
Can be coloured with two colours (straight cross-overs) 1150
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 239 708
square 712 1800
regular pentagon 229 3126
regular hexagon 300 476
regular heptagon 24 84
regular octagon 191 261
regular enneagon 6 6
regular decagon 5 9
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 45.0 179 1026
2 48.0 1 1
2 50.0 2 2
2 51.4 4 8
2 52.5 1 2
2 58.5 1 1
2 60.0 166 283
2 63.0 1 1
2 66.0 1 1
2 67.5 2 8
2 70.0 2 2
2 72.0 91 942
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 5 5
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 80 114
4 48.0 1 1
4 51.4 1 3
4 52.5 1 1
4 54.0 4 4
4 60.0 37 39
4 63.0 1 1
4 64.3 5 6
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 52 341
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 60.0 213 243
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 45 46
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 10 11
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 45.0 126 257
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 2 2
8 71.3 3 3
8 72.0 5 5
8 73.1 1 1
8 75.0 6 6
8 76.5 1 1
8 80.0 2 2
8 90.0 527 1416
8 100.0 2 4
8 105.0 6 6
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 4 4
10 54.0 1 1
10 72.0 113 193
10 85.5 1 1
10 90.0 2 2
10 98.0 1 1
10 108.0 86 282
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 60.0 139 174
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 2 2
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 77 79
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 3 3
16 73.1 1 1
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
- 88
0.38 1
0.50 4
1.00 5
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 1
3.00 9
3.21 3
3.75 14
4.29 4
4.50 6
5.00 37
5.63 1
6.00 13
6.43 1
7.50 86
8.57 4
9.00 11
10.00 13
11.25 20
12.00 11
12.86 6
15.00 232
18.00 31
20.00 16
22.50 251
25.71 30
30.00 321
36.00 244
45.00 637
60.00 197
90.00 253
120.00 17

7  Does the pattern satisfy the two polygon condition?

Property Number
False 2419
True 185

8  The interlace condition

Finite interlaces Infinite interlaces Total
-1 0 69
0 0 1398
0 1 222
0 2 167
0 3 35
0 4 21
0 5 3
0 6 1
0 8 1
1 0 125
1 1 129
1 2 53
1 3 4
1 4 1
1 5 3
1 7 1
2 0 103
2 1 66
2 2 13
2 3 8
2 4 1
2 5 1
3 0 46
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 16
5 1 10
5 2 2
6 0 8
6 1 7
7 0 7
7 1 2
7 4 1
8 0 3
8 2 2
9 0 3
10 1 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 1 140
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 89
1 0 0 416
1 0 1 22
1 0 2 6
1 0 4 2
1 1 0 33
1 2 0 2
1 3 0 3
2 0 0 254
2 0 1 5
2 0 2 3
2 0 3 1
2 0 6 1
2 1 0 24
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 0 292
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 0 175
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 0 143
5 0 2 1
5 1 0 22
5 2 0 2
5 3 0 2
6 0 0 88
6 1 0 24
6 2 0 4
6 4 0 1
7 0 0 72
7 0 2 3
7 1 0 18
7 2 0 3
7 3 0 1
7 4 0 1
8 0 0 49
8 1 0 14
8 2 0 6
8 3 0 3
8 4 0 1
9 0 0 35
9 0 2 1
9 1 0 13
9 2 0 3
9 4 2 1
10 0 0 31
10 1 0 7
10 2 0 4
10 4 0 1
11 0 0 16
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 4
15 0 0 3
15 1 0 7
15 2 0 4
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 1
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 575
True 2030

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
copple 1
creswell 16
critchlow 24
cromwell1 1
cromwell2 2
cromwell3 1
d-avennes 41
dawes 174
degeorge2 46
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 9
gands 113
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 15
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
orazi 4
orton 1
otto 1
paccard 91
pajares 25
pavon 10
pc 623
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 96
sourdel 3
stevens 23
stierlin 3
stierlin2 1
stock 6
stronge 20
sutton 7
useinov 3
vami 50
viollet 1
volwah 2
wade 58
wadei 388
wahhab 34
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 1443 of these.

13  Photographic links

There are 716 tiling patterns whose records link to a photograph. The total number of links to photographs is 1018.

14  Version records

Version Date TilingsComment
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 2336See.
30 2013-08-08 2304See.
29 2013-05-01 2304See.
28 2013-02-19 2278See.
27 2012-12-16 2235See.
26 2012-10-16 2201See.
25 2012-08-21 2151See.
24 2012-05-28 2020See.
23 2012-02-11 1983See.
22 2011-12-17 1941See.
21 2011-09-19 1908See.
20 2011-06-21 1868See.
19 2011-02-28 1829See.
18 2010-11-15 1771See.
17 2010-08-14 1727See.
16 2010-05-07 1695See.
15 2010-01-29 1646See.
14 2009-12-09 1601See.
13 2009-10-09 1563See.
12 2009-06-20 1499See.
11 2009-03-05 1442See.
10 2009-01-03 1403See.
9 2008-11-16 1353See.
8 2008-09-29 1319See.
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