α: 0.207163
S_4: sqrt(3 / 4 - cos(α) / sqrt(2))
S_3: sqrt(3 / 4 + cos(α) / sqrt(2))
S_1: sqrt(((((sqrt(2) + sqrt(2 + (sqrt(2) * cos(α))) + sqrt(2 - (sqrt(2) * cos(α)))) * ((-sqrt(2)) + sqrt(2 + (sqrt(2) * cos(α))) + sqrt(2 - (sqrt(2) * cos(α))))) * (sqrt(2) - sqrt(2 + (sqrt(2) * cos(α))) + sqrt(2 - (sqrt(2) * cos(α))))) * (sqrt(2) + sqrt(2 + (sqrt(2) * cos(α))) - sqrt(2 - (sqrt(2) * cos(α)))))) / 4
r: sin(α) / ((2 * S_1) + S_3 + S_4)
b: (r * sqrt(1 + (2 * sin(α)^(2))))
A: (0, 0, 0)
B_1: (1, 0, 1)
C: (1 + cos(α) / sqrt(2), sin(α), cos(α) / sqrt(2))
D_1: (cos(α) / sqrt(2), sin(α), 1 + cos(α) / sqrt(2))
棱锥, face4, face2, face1, face3, edge4, edge3, edge5, edge2, edge1, edgeAC = Pyramid(D_1, B_1, C, A)
a: (((b * csc(α)) * (sqrt(3 + ((2 * sqrt(2)) * cos(α))) + sqrt(((2 + csc(α)^(2)) * sin(α)^(2))) + ((sqrt(2) * cos(α)) * sqrt(((2 + csc(α)^(2)) * sin(α)^(2))))))) / ((2 * sqrt(((2 + csc(α)^(2)) * sin(α)^(2)))))
I: (a, b, a)
G: (1 / 2 + cos(α) / ((2 * sqrt(2))), sin(α) / 2, 1 / 2 + cos(α) / ((2 * sqrt(2))))
GI = Distance(G, I)
误差: GI - r
IG = Distance(I, G)