From the circle to the icosahedron

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Knoll, Eva
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Bridges: Mathematical Connections in Art, Music, and Science
The following exercise is based on experiments conducted in circular Origami. This type of paper folding allows for a completely different geometry than the square type since it lends itself very easily to the creation of shapes based on 30-60-90 degree angles. This allows for experimentation with shapes made up of equilateral triangles such as deltahedra. The results of this research were used in Annenberg sponsored activities conducted in a progressive middle school in Houston TX, as well as a workshop presented at the 1999 Bridges Conference in Winfield, KS. Not including preparatory and follow up work by the teacher, the activities in Houston were composed of two main parts, the collaborative construction of a three-yard-across, eighty-faced regular deltahedron (the Endo- Pentakis Icosi-dodecahedron) and the following exercise. The barn-raising was presented last year in Winfield, and the paper folding is the topic of this paper.
Circular Origami , Origami
Knoll, E. (2000b). From the Circle to the Icosahedron. In Sarhangi, R., (Ed.), Bridges: Mathematical Connections in Art, Music and Science, pp. 231-237.