Cox's Theorem

Let sigma_1, ..., sigma_4 be four planes in general position through a point P and let P_(ij) be a point on the line sigma_i·sigma_j. Let sigma_(ijk) denote the plane P_(ij)P_(ik)P_(jk). Then the four planes sigma_(234), sigma_(134), sigma_(124), sigma_(123) all pass through one point P_(1234). Similarly, let sigma_1, ..., sigma_5 be five planes in general position through P. Then the five points P_(2345), P_(1345), P_(1245), P_(1235), and P_(1234) all lie in one plane. And so on.

See also

Clifford's Circle Theorem, Cox Configuration, Plane

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Cite this as:

Weisstein, Eric W. "Cox's Theorem." From MathWorld--A Wolfram Web Resource.

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