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The Orbifold Shop (Geometry and the Imagination)

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Author:Conway, Doyle, Gilman, Thurston; The Geometry Center
Description: A symmetry project: the Orbifold Shop offers a free coupon for $2.00 worth of parts, installation included, to anyone acquiring a new orbifold. There are only a few kinds of features for two-dimensional orbifolds, but they can be used in combinations: handle, mirror, cross-cap, order n cone point, order n corner reflector... If you exactly spend your coupon, you will have a quotient orbifold coming from a symmetrically repeating pattern in the Euclidean plane with a bounded fundamental domain. There are exactly 17 different ways to do this, corresponding to the 17 different symmetrically repeating patterns with bounded fundamental domain in the Euclidean plane... What combinations of parts can you find that cost exactly $2.00?

Levels: Middle School (6-8), High School (9-12), College
Languages: English
Resource Types: Problems/Puzzles
Math Topics: Symmetry/Tessellations

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