Mathematics Resources by Topic - Space
Tessellations
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tessellation of triangle - Flash movie
All triangles tessellate using rotation and translation.

tessellation of quadrilateral - Flash movie
All quadrilaterals tessellate using rotation and translation.

tessellation of quadrilateral
Drag the vertices of the "model" quadrilateral and see how its images tessellate the plane.

shapes to tessellate on square and isometric grids - CIMT (pdf file)

tessellations with kangaroos, sheep, koalas, platypus, yabbies, ... - Bruce Bilney

For a detailed exploration of tessellations, go to these great sites:

resources from the Totally Tessellated site
regular polygons for cutting out, tessellations with regular polygons, grids

Tyler - Java applet
Tessellate regular polygons with 3,4,5,6,8,9,10,11,12 sides - can be downloaded.

Tessellation Tool
Tessellate regular polygons with 3,4,6,8 sides.

tessellation applets - Project Interactive

Circle applet
Create tessellations of overlapping circles (example).

Tiling Transformer
Start with a tiling of squares or regular hexagons. Perform repeated transformations - insert triangles, quadrilaterals or pentagons, draw the dual tiling.

Escher Web Sketch - Java applet
Draw patterns based on the 17 different plane symmetry groups.

Kali - Java applet
Create patterns based on symmetry groups - 11 rosette, 7 frieze and 17 wallpaper groups (can be downloaded).

Kali software
Create patterns based on symmetry groups - 11 rosette, 7 frieze and 17 wallpaper groups.

Tess software
Create patterns based on symmetry groups - 11 rosette, 7 frieze and 17 wallpaper groups.

Kaleidotile software
Explore tessellations of the sphere, Euclidean plane and hyperbolic plane.

TesselMania software
free software and examples for Escher type tessellations

Escher

Polypolygon Tilings - Steven Dutch
tessellations of polyominoes, polyiamonds and polyhexes

Isohedral Tilings by Symmetric Polygonal Tiles - Doris Schattschneider
interactive diagrams of 42 types of tessellation made with single polygons that have reflective or rotational symmetry

Encyclopedia of Fractal Tilings - Robert Fathauer
Robert Fathauer combines the topics of tiling and fractals. The encyclopedia is an attempt to describe all distinct fractal tilings of the plane. See also the Mathematical Art of Robert Fathauer.

Islamic tessellations

Taprats - Craig Kaplan
Java applet that implements one design technique for Islamic star patterns - can be downloaded

Isohedral Tilings by Symmetric Polygonal Tiles - Doris Schattschneider
interactive diagrams of 42 types of tessellation made with single polygons that have reflective or rotational symmetry

Intriguing Tessellations - Marjorie Rice
Marjorie Rice discovered four new tessellating pentagons in the late 1970's.  So far only fourteen types of convex pentagon that tile the plane have been found.

Origami Tessellations - Alex Bateman

Penrose tiles

Spidron - Daniel Erdely
A plane-filling object (Spidron) consists of an infinite number of equilateral triangles and 120°,30°,30° isosceles triangles. Each equilateral triangle is joined with an isosceles triangle of 1/3 the area and this isosceles triangle is joined with another equilateral triangle having an area equal to the area of the isosceles triangle ...

tessellations based on 17 wallpaper symmetry groups - symmetry patterns / groups resources page

Student Tessellations - links

Tessellations - collection of links - Jill Britton

Tilings - collection of links - Geometry Junkyard