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a: 1
A: (0, ((2 * sqrt(3)) * a / 3), 0)
B: ((-a), ((-sqrt(3)) * a / 3), 0)
C: (a, ((-sqrt(3)) * a / 3), 0)
D: (0, 0, ((2 * sqrt(2)) * a / sqrt(3)))
O: (0, 0, a / sqrt(6))
b = Sphere(O, a / sqrt(6))
f = Segment(D, B)
g = Segment(B, C)
h = Segment(C, D)
i = Segment(A, C)
j = Segment(D, A)
k = Segment(A, B)
c = Sphere(O, (sqrt(6) * a / 2))
P = 0 (slider from 0 to 1, step 1)
text1: "" + (LaTeX[If[P ≟ 0, "内接球", "外接球"]]) + ""
E = Midpoint(B, C)
d = Plane(A, D, E)
u = OrthogonalVector(d)