#------------------------------------------------------[br]# Construct red and green bands (given red)[br]# The center of the green band is halfway[br]# along the edge of the icosihedron.[br]#------------------------------------------------------[br][br]O = (0,0,0)[br]sph = Sphere(O,1)[br]Rcenter = (1,0,0)[br][br]red = 10.61369513431076°[br][br]γ = atand(tan(red) / cos(54°))[br][br]R01 = (cos(γ), 0, sin(γ))[br]R03 = Rotate(R01, -72°, xAxis)[br]axisR = Line(O, Vector(Vector(O, R01) ⊗ Vector(O, R03)))[br]R02 = Rotate(R01, red, axisR)[br]R04 = Rotate(R01, 3*red, axisR)[br][br]G01 = Rotate(R02, -72°, xAxis)[br]G02 = R04[br]green = Angle(G01, O, G02)[br]axisG = Line(O, Vector(Vector(O, G01) ⊗ Vector(O, G02)))[br]Gmid = Rotate(G01, 1.5*green, axisG)[br]G04 = Rotate(G01, 3*green, axisG)[br][br]Rarc = CircularArc(O, R01, R04, Plane(O, R01, R04))[br]Rarc5= Zip(Rotate(Rarc, k * 72°, xAxis), k, 0..4)[br]Garc = CircularArc(O, G01, G04, Plane(O, G01, G04))[br][br]# α is 2*distance Rcenter Gmid[br]#---------------------------------- [br]α = 2*Angle(Rcenter, O, Gmid)[br][br]# β is edge of the icosihedron[br]#---------------------------------- [br]β = acosd(sqrt(1/5))[br][br]# If red is correct,[br]# the difference should be 0[br]#---------------------------------- [br]δ = α - β[br][br]#------------------------------------------------------[br]# Compare [1/3] with [2/3][br]#------------------------------------------------------[br]red23 = 14.495596141331275°[br]green23 = 16.289240170644682°[br][br]factRed = red / red23[br]factGreen = green / green23[br][br]

The rotegrity "straps" (of the same color) are the same length/width[br](but bent to different radii, of course, producing different-size spheres.)[br][br]In 3D-modeling, I refer to the two different size rotegrities as "greater" and "lesser",[br]to keep my model files organized. Technically, they are, both, Class-II, 2v rotegrities.[br][br]The ratio of sphere radii is about 1:¾[br]

The rotegrity "straps" (of the same color) are NOT the same length/width[br][br]red [1/3] : red [2/3] = 0.732201[br]green [1/3] : green[2/3] = 0.762272