Imagine, Geometry -- icosahedron, 31 great circles

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These pages are to give flight to your imagination.

Buckminster Fuller inspires fascination with geodesics, the odyssey of adventuring in, around, and about the meanings of great circles. He found 31 great circles related to the icosahedron (see section 457 in Synergetics). Here they are as red, green, and blue strings. Each string is an equatorial circle of the axis of a pair of features of the solid. The great circles are the equators of the axes of spin of opposite pairs of features. There are:

  • 15 axes of the 30 edges (green)
  • 6 axes of the 12 vertexes (red)
  • 10 axes of the 20 faces (blue)
This image is the flat version of the QTVR model of the interior of the 31 circles. Click to enter.

equatorial circle map
See QuickTime for information and a listing of all the QTVRs here.

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