xy平面截正8面體
Author: kuanchangsou

阿壽工坊---http://120.101.70.8/longlife/

平面對正八面體的截痕:

a = 8 (slider from 1 to 10, step 0.1)
θ = 1.9106332362490186 rad
h = 0 (slider from -10 to 10, step 0.1)
b: (a / 2 / sqrt(3) * tan(θ / 2))
O: (0, 0, h)
H: O + (0, 0, (-b))
c: (a / 2 * sec(30°))
A: (c, 0, h - b)
B: ((c * cos(120°)), (c * sin(120°)), h - b)
α = 0 rad (slider from 0 to 6.283185307179586, step 1*°)
β = 0 rad (slider from 0 to 6.283185307179586, step 1*°)
γ = 0 rad (slider from 0 to 6.283185307179586, step 1*°)
d = Segment(O - (6 * (cos(α), sin(α), 0)), O + (6 * (cos(α), sin(α), 0)))
H' = Rotate(Rotate[H, β, d], γ, Line[(0, 0, 0), (0, 0, 1)])
A' = Rotate(Rotate[A, β, d], γ, Line[(0, 0, 0), (0, 0, 1)])
B' = Rotate(Rotate[B, β, d], γ, Line[(0, 0, 0), (0, 0, 1)])
f = Line((0, 0, 0), (0, 0, 1))
e, C, D, E, F, faceA'B'C, faceA'CF, faceA'DF, faceA'B'D, faceB'DE, faceB'CE, faceCEF, faceDEF, edgeA'C, edgeA'B', edgeB'C, edgeA'F, edgeCF, edgeA'D, edgeDF, edgeB'D, edgeB'E, edgeDE, edgeCE, edgeEF = Octahedron(A', B', Vector[H', O])
poly1, G, I, J, K, L, M, g, i, j, k, l, m = IntersectPath(xOyPlane, e)