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Heptagonal Ring

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Heptagonal Ring
http://farm1.static.flickr.com/206/521556809_b1ef7f62a6.jpg
Nice Try: misses by ten degrees or so
TypeRing
Panels 7 × Geomag square panel icon
Rods 100 × Geomag rod icon
Spheres 30 × Geomag ball icon
Author Karl Horton 14:42, 30 May 2007 (UTC)


More pictures on flickr

Calculations Edit

Let

  • α = arccos(√(1/3)) = 54.736° = inclination of face of square base pyramid.
  • φ = arccos(1/3) = 70.529° = apex angle of square based pyramid.
  • Note the identity: 2α + φ = 180°

Observe one of the heptagonal elements, and move through the angles in the structure, counting the rotation as you go:

  • rotation = φ + α + 60° + α + φ
  • simplify = 240° + φ

So, the residual angle from 360° is the angle between the edges of the module:

  • Module angle = 360° - 240° - φ = 120° - φ = 49.471°

Seven elements leave a residual slice of pie of angle 13.70°

Which is too much for the structure to flex into.

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