Tiling and Tessellation

Semi-regular Tessellation

Squares and Equilateral Triangles

worksheet

Tessellation with Convex Hexagons

 

Type 1

B = D = F = 120 deg

AB = BC; CD = DE; EF = FA

worksheet for a transformation exercise based on this tessellation

 

Type 2

B+C+D = 360 deg

AB = DE

 

Type 3

A+B+D = 360 deg

AF = CD; BC = DE

 

A Special Case of Type 2

3 pairs of opposite sides equal and parallel

 

Tessellation with Convex Pentagons

 

Type 1

B+C+D =360 deg

 

Type 2

A+B+D = 360 deg

AE = DC

 

Type 3

A = B = D = 120 deg

CD = DE; CA + BE = AB

 

Type 4

A = C = 90 deg

EA = AB; BC = CD

 

Type 5

A = 60 deg; C = 120 deg

EA = AB; BC = CD

 

Type 6

A+B+D = 360 deg; A = 2C

DE = EA = AB; BC = CD

 

Type 7

2D+A = 360 deg; 2B+C = 360 deg

EA = AB = BC = CD

 

Special Case of Type 2

E = C = 90 deg

AE = DC; ED = BC

 

Special Case of Type 2 and 4

E = C = 90 deg

AE = ED = DC = CB

AB can be adjusted until all sides equal (Cairo Street Tiling)

 

Tessellation with Concave Pentagons; Rotational Symmetry

 

Regular Decagon (Colored and Outline)

composed of equilateral pentagons

worksheet for investigating number of pentagons in successive rings

  Regular Octagon
  Regular Nonagon
   

 


Reference

Web

Totally Tessellated - A ThinkQuest Internet Challenge 1998 Entry
http://library.thinkquest.org/16661/index2.html
 
Tessellation Tutorials by Suzanne Alejandre at the Math Forum
http://www.DrMath.com/sum95/suzanne/tess.intro.html
 
Tessellations Theme Page at Community Learning Network
http://www.cln.org/themes/tessellations.html

links to information about tessellations (curricular resources and instructional materials)

 
Tantalizing Tessellations
http://mathcentral.uregina.ca/RR/database/RR.09.96/archamb1.html

series of lesson plans integrating tessellations across the curriculum

 
Tessellations: Creative Combinations of Math, Art and Fun (at mathartfun.com)
http://www.tessellations.com/
 
Catalog of Isohedral Tilings by Symmetric Polygonal Tiles by Doris Schattschneider and Nikolai Dolbilin
http://forum.swarthmore.edu/dynamic/one-corona/

rather technical article but full of interesting dynamic illustrations with The Geometer's Sketchpad, showing tilings of various symmetric quadrilaterals, pentagons and hexagons

 

Intriguing Tessellations by Marjorie Rice: Discovery and Designsof Convex Pentagon Tessellations
http://members.aol.com/tessellations/index.html

 
Pentagons that tile the Plane
http://burtleburtle.net/bob/tile/pentagon.html

it talks about all kinds of pentagons (concave and convex) and a 'recipe' for finding the tiles

 
The 14 Different Types of Convex Pentagons that Tile the Plane
http://www.mathpuzzle.com/tilepent.html
 
Tessellation Resources at Geometry Centre
http://www.geom.umn.edu/software/tilings/

2 lists of online resources complied by Prof. Doris Schattschneider: references and sources for illustrations; software for creating tilings

 
Grotesque Geometry by Andrew Crompton
http://www.cromp.com/tess/home.html

art work inspired by those of Escher and a list of artists doing similar things

 
Internet Lesson Plans by artist/teacher Woody Duncan
http://www.taospaint.com/Tessellation.html
 
Escher Web Sketch
http://www-sphys.unil.ch/escher/

a Java applet for drawing repeating patterns with various symmetry; you may work online or download the applet

 
Penrose Tiler: a Java applet for creating and investiagting Penrose Tilings
http://solar.aie.nl/~geert/java/public/Penrose.html
 

 

Books

Gardner, M. (1988), Time Travel and Other Mathematical Bewilderments, New York: W.H. Freeman and Company.
(Ch. 13, Tiling with Convex Polygons)

 
Nelson, D., Joseph, G.G., Williams, J. (1993), Multicultural Mathematics, Oxford: Oxford Unversity Press.
(Ch. 6, Geometry and Art).
 
Wells, D. (1991), The Penguin Dictionary of Curious and Interesting Geometry, Penguin Books.