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