perplexus.info :: Geometry : Points and Planes

Points and Planes (Posted on 2004-12-17)

Given four non-coplanar points, how many different planes exist that are equidistant from all four points?

Submitted by Bractals

Rating: 3.3333 (3 votes)

Solution: (Hide)

Seven. Consider the four points as the vertices of a tetrahedron. Four planes each parallel to a face and halfway between the face and the opposite vertex. Three planes each parallel to opposite edges and halfway between them.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: solution	McWorter	2005-02-26 00:34:00
solution	McWorter	2005-02-26 00:31:03
No Subject	daniel	2004-12-18 00:37:19
re: Equidistance?	Larry	2004-12-17 22:58:44
Equidistance?	CeeAnne	2004-12-17 19:20:33
re: I'm pretty sure Jer is right...	Larry	2004-12-17 17:17:50
re(2): Initial thoughts + conjecture (spoilers)	SteveH	2004-12-17 17:17:43
I'm pretty sure...	Jer	2004-12-17 17:13:50
re: Initial thoughts + conjecture (spoilers)	Larry	2004-12-17 16:30:17
Initial thoughts (spoilers)	nikki	2004-12-17 15:42:53

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