Making a lamp
Doing the math
The only way I can see to figure the dihedral angle is to work from the 2-fold symmetry:
- Start with a golden rectangle with corners A, B, C, D.
- Golden ratio (GR:1) = 1/2(sqrt+1):1 = 1.6180.
- Assume AB = 12, then AD = 19.4164.
- Bisect the first golden rectangle with another golden rectangle with endpoints EF so that G splits AD into two.
- AG = AD/2 = 9.7082.
- EF - AB = x = 7.4164.
- x/2 = GF = Adjacent = 3.7082.
- GF² + AG² = AF² = 13.7507 + 94.2492 = 107.9999.
- AF = Hypotenuse = 10.3923.
- Cosine = Adjacent/Hypotenuse = 0.3568.
- AFG = 69.0948.
- 2(AFG) = AFD = Dihedral angle = 138.19 (138º 11').