Six-Sphere Coordinates

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The six-sphere coordinate system inverts Cartesian coordinates. The inverted coordinates correspond to the intersection of three constant coordinate surfaces. A line passing through this intersection connects the origin with the initial coordinates. Show all six spheres including those corresponding to constant initial coordinates reflected at the origin.
Contributed by: Michael Schreiber (March 2011)
Open content licensed under CC BY-NC-SA
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"Six-Sphere Coordinates"
http://demonstrations.wolfram.com/SixSphereCoordinates/
Wolfram Demonstrations Project
Published: March 7 2011