KaleidoTile

Reflecting on Symmetry

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:


This page contains information on the following topics:

History

KaleidoTile was adapted for the Apple Macintosh by Jeff Weeks from Triangle Tiling, a program developed and copyrighted by the Geometry Center for a display at the St. Paul Science Museum. Both programs are freely available for non-comercial use, and may be downloaded from the Geometry Center.

KaleidoTile is currently being adapted for use with Microsoft Windows.

The KaleidoTile Project

During the Geometry Center's summer 1995 Teacher Program, a team of four teachers and three undergraduates created some curriculum materials, including this web site, based on the software package KaleidoTile.

Sample Materials

Lesson 3: Reflecting with One Mirror & Dihedral Symmetry
Break out those mirrors! Examine reflective, rotational, and dihedral symmetry using two mirrors.

Lesson 11: Introduction to KaleidoTile
A beginner's guide to using the program KaleidoTile.

Lesson 12: Naming Polyhedra
In KaleidoTile, 19 Archimedean solids put in appearances. Which ones? How are they related? Find out by completing these activities using KaleidoTile.

Lesson 14: Discovering Symmetry with KaleidoTile: Symmetries of the Plane
So how do symmetry and KaleidoTile fit together? Find the bonds here. This is a good way to gain experience on KaleidoTile.


In addition to these lessons, other resources are available:

Any feedback on this site, or the project in general, should be adressed to webmaster@geom.umn.edu.

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Last updated: 24 January 1996
Copyright © 1995 by The Geometry Center, all rights reserved.