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6 - Constructing dipyramids and rotating rings from straight strips of triangles

Published online by Cambridge University Press:  10 November 2010

Peter Hilton
Affiliation:
State University of New York, Binghamton
Jean Pedersen
Affiliation:
Santa Clara University, California
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Summary

Required materials

  • About 10 yards (10 meters) of 2-inch (5 cm) gummed mailing tape (or a longer length of wider tape if you want larger models). The glue on the tape should be the type that needs to be moistened to become sticky. Don't try to use tape that is sticky to the touch when it is dry – if you do you will find the experience very frustrating.

  • Two different colors of brightly colored wrapping paper or butcher paper

  • Scissors

  • Sponge (or washcloth)

  • Shallow bowl

  • Water

  • Hand towel (or rag)

  • Some big (heavy) books

  • Some bobby pins, or rubber bands

Preparing the pattern piece for a pentagonal dipyramid

Begin by folding some of the gummed mailing tape using the U1D1-folding procedure as shown in Section 2.3. Do this with the gummed side up, so you can see your fold lines better – and so that the paper will “curl” in the right direction when you assemble the model. Continue folding until you have 40 or more triangles. Cut or carefully tear the tape on the last fold line. Then cut off, or tear off, a strip containing 31 triangles counting from this end (that is, not from the end from which you began the folding).

Next place your strip of 31 equilateral triangles so that one end appears as shown in Figure 6.1 with the gummed side down.

Type
Chapter
Information
A Mathematical Tapestry
Demonstrating the Beautiful Unity of Mathematics
, pp. 86 - 95
Publisher: Cambridge University Press
Print publication year: 2010

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