Nex21 (4,1) [1/3] - Solve
Source Code
#------------------------------------------------------
# Construct red and green bands (given red)
# The center of the green band is halfway
# along the edge of the icosihedron.
#------------------------------------------------------
O = (0,0,0)
sph = Sphere(O,1)
Rcenter = (1,0,0)
red = 10.61369513431076°
γ = atand(tan(red) / cos(54°))
R01 = (cos(γ), 0, sin(γ))
R03 = Rotate(R01, -72°, xAxis)
axisR = Line(O, Vector(Vector(O, R01) ⊗ Vector(O, R03)))
R02 = Rotate(R01, red, axisR)
R04 = Rotate(R01, 3*red, axisR)
G01 = Rotate(R02, -72°, xAxis)
G02 = R04
green = Angle(G01, O, G02)
axisG = Line(O, Vector(Vector(O, G01) ⊗ Vector(O, G02)))
Gmid = Rotate(G01, 1.5*green, axisG)
G04 = Rotate(G01, 3*green, axisG)
Rarc = CircularArc(O, R01, R04, Plane(O, R01, R04))
Rarc5= Zip(Rotate(Rarc, k * 72°, xAxis), k, 0..4)
Garc = CircularArc(O, G01, G04, Plane(O, G01, G04))
# α is 2*distance Rcenter Gmid
#----------------------------------
α = 2*Angle(Rcenter, O, Gmid)
# β is edge of the icosihedron
#----------------------------------
β = acosd(sqrt(1/5))
# If red is correct,
# the difference should be 0
#----------------------------------
δ = α - β
#------------------------------------------------------
# Compare [1/3] with [2/3]
#------------------------------------------------------
red23 = 14.495596141331275°
green23 = 16.289240170644682°
factRed = red / red23
factGreen = green / green23
TaffGoch (12 dec 2016)
The rotegrity "straps" (of the same color) are the same length/width
(but bent to different radii, of course, producing different-size spheres.)
In 3D-modeling, I refer to the two different size rotegrities as "greater" and "lesser",
to keep my model files organized. Technically, they are, both, Class-II, 2v rotegrities.
The ratio of sphere radii is about 1:¾
Thijs (18 jun 2023)
The rotegrity "straps" (of the same color) are NOT the same length/width
red [1/3] : red [2/3] = 0.732201
green [1/3] : green[2/3] = 0.762272