The KaleidoTile program is a tool for creating and manipulating tessellations of the sphere, Euclidean plane, and hyperbolic plane by triangles. A special feature changes these 'curved' patterns into 'flat' ones. With this feature, spherical tilings become polyhedra, 19 of which are Archimedean.

By manipulating these tessellations, students can explore a wide range of topics, including:

dihedral symmetry
duality
spherical, hyperbolic, and Euclidean geometry
polyhedra names
angle measure

This page contains information on the following topics:

• History
  
• The KaleidoTile Project
  
• Links to the materials
  
• About this site
  

KaleidoTile is currently being adapted for use with Microsoft Windows.

The result was KaleidoTile: Reflecting on Symmetry, a unit aimed at students in grades 6-10 and focusing on the fundamental concept of symmetry. It is a gradual development of the concepts behind KaleidoTile as well as an introduction to the use of the program. The materials produced include:

• a 5 minute video, Mad About Mirrors
  
• 16 class lessons
  
• this Web site
  

The lessons follow a number of separate strands. Lessons 1-5 focus on symmetries of the plane, especially reflective symmetry. Lesson 6 is a culmination of these concepts, with instructions on building kaleidoscopes out of glass mirrors.

Polyhedra become the focus of lessons 7-9. In these lessons students build polyhedra out of readily available materials. Lesson 10 serves to tie the preceding lessons together, by including activities in which 3-dimensional patterns are built using mirrors.

KaleidoTile is formally introduced in lessons 11-13. These lessons can be used outside of the unit as an introduction to the program.

Finally, the connections amongst these topics are resolved, and new questions are raised, by lessons 14-16.

Each lesson contains a Teacher's Guide; most, but not all, contain Activity Sheets and corresponding Answer Keys.

The entire unit is being made available to the public free of charge by the Geometry Center. Click here to download Lessons 1-16. In addition, the complete KaleidoTile unit materials, including the video, can be obtained by writing to the Geometry Center:

A selection of these materials has been placed on this Web site. These include lessons that meet one or more of the following criteria:

• They are stand-alone.
  
• They look flashy.
  
• They can be used as an introduction to the software.
  

The lessons we have included are:

In addition to these lessons, other resources are available:

• A list of References to Web sites, books, and other inspirational sources.
  
• Since the video Mad About Mirrors is not available online, we have done the next best thing - here is a link to the Mad About Mirrors page. The page contains MPEG clips, as well as stills, from the video.
  
• Polyhedra reference chart, putting valuable information at your fingertips.
  

Last updated: 12 August 1995
Copyright © 1995 by The Geometry Center, all rights reserved.