| 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) |
More pictures on flickr
Calculations[]
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.