# Some statistics: Version 52

## 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 *442 (p4m) 1025 The symmetry group of the tiling is 2*22 (cmm) 293 The symmetry group of the tiling is *632 (p6m) 522 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 *333 (p3m1) 21 The symmetry group of the tiling is *8• (d8) 17 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 3*3 (p31m) 35 The symmetry group of the tiling is *6• (d6) 6 The symmetry group of the tiling is 6• (c6) 19 The symmetry group of the tiling is *5• (d5) 13 The symmetry group of the tiling is *2222 (pmm) 184 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 not symmetric and hence is not a repeat pattern 82 The symmetry group of the tiling is 2• (c2) 34 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 2*∞ (pmg) 2 The symmetry group of the tiling is *16• (d16) 1 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 845 Can be coloured with two colours 263 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 Tilings Total 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 70 0 0 1480 0 1 233 0 2 173 0 3 44 0 4 22 0 5 5 0 6 3 0 8 3 1 0 135 1 1 155 1 2 55 1 3 8 1 4 1 1 5 3 1 7 1 2 0 138 2 1 71 2 2 16 2 3 9 2 4 1 2 5 1 3 0 72 3 1 23 3 2 5 4 0 25 4 1 18 4 2 10 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 tiles Reflective pairs No mirror image Number 0 0 0 239 0 0 1 154 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 0 101 1 0 0 420 1 0 1 21 1 0 2 1 1 0 4 2 1 0 6 1 1 1 0 45 1 2 0 2 1 3 0 3 2 0 0 280 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 0 158 5 0 2 1 5 1 0 26 5 2 0 3 5 3 0 2 6 0 0 103 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 40 9 0 2 1 9 1 0 14 9 2 0 4 9 5 0 1 10 0 0 34 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 3 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 7 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 601 True 0

## 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 Tilings Comment 52 2021-08-15 2862 See. 51 2020-11-23 2857 See. 50 2020-08-01 2840 See. 49 2019-08-01 2811 See. 48 2019-03-15 2812 See. 47 2018-09-29 2767 See. 46 2018-07-22 2717 See. 45 2018-05-15 2714 See. 44 2017-12-28 2690 See. 43 2017-09-10 2670 See. 42 2016-09-27 2620 See. 41 2016-05-14 2603 See. 40 2016-02-01 2566 See. 39 2015-11-28 2548 21 new patterns 38 2015-09-04 2527 Negative searching 37 2015-04-20 2517 New search facility 36 2014-11-29 2510 Interlace counts 35 2014-08-03 2505 James William Wild 34 2014-06-06 2429 Chelates 33 2014-03-08 2440 Variant patterns 32 2013-12-11 2389 Kites and Darts 31 2013-10-08 2336 More patterns from Iran 30 2013-08-08 2304 All patterns have a PDF version 29 2013-05-01 2304 Patterns from Nick Crossling added 28 2013-02-19 2278 Patterns from Alberto Leon added 27 2012-12-16 2235 Patterns in Islamic style added from Tony Lee 26 2012-10-16 2201 More Roman mosaic patterns added 25 2012-08-21 2151 Roman mosaic patterns added 24 2012-05-28 2020 More paterns from the Alhambra added 23 2012-02-11 1983 More pattern added from David Wade's photos 22 2011-12-17 1941 More patterns from Borgoin added 21 2011-09-19 1908 Patterns with borders added 20 2011-06-21 1868 Example of internal documentation provided 19 2011-02-28 1829 25 patterns from Tony Lee 18 2010-11-15 1771 More paterns from the Alhambra added 17 2010-08-14 1727 Large JPG display added for some patterns 16 2010-05-07 1695 Some V and A material added 15 2010-01-29 1646 Entry page display added 14 2009-12-09 1601 Tilings of a square with similar triangles added 13 2009-10-09 1563 Two-uniform tilings added 12 2009-06-20 1499 Patterns from Borgoin added 11 2009-03-05 1442 Patterns on the Alhambra added 10 2009-01-03 1403 Random display of 20 patterns added 9 2008-11-16 1353 Limks to David Wade's photos added 8 2008-09-29 1319 Polyominoes tilings added 7 2008-06-22 1190 Tree search and Conway-Thurston notation 6 2008-05-05 1178 Tilings from Stevens 5 2008-03-31 1153 Islamic tilings from DeGeorge 4 2008-02-23 1130 Spiral tilings added 3 2007-12-27 1106 Further Islamic tilings added 2 2007-11-05 1085 First version on Internet 1 2007-10-06 1076 Islamic tiling added 0 2007-08-26 1050 Initial system