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Four Points Determine a Sphere

​
index of a
9
{0,-2,0}
index of b
15
{-2,-2,-1}
index of c
20
{-2,1,2}
index of d
31
{1,-2,-2}
center = -
1
2
,
3
2
,-
3
2
radius =
59
2
Four noncoplanar points define the surface of a sphere. Each point runs through the 343 possible triples, indexed by
(x,y,z)
where
x,y,z∈{-3,-2,-1,0,1,2,3}
.
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