Divisions of space by parallels

Alexanderson, G. L.; Wetzel, John E.

doi:10.1090/S0002-9947-1985-0797066-2

Divisions of space by parallels
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by G. L. Alexanderson and John E. Wetzel PDF

Trans. Amer. Math. Soc. 291 (1985), 363-377 Request permission

Abstract:

An arrangement of hyperplanes in ${\mathbb {E}^d}$ is a "plaid" provided its hyperplanes form no multiple flats of intersection and lie in parallel families that are in general position. We develop some geometrically natural formulas for the number of $r$-faces that are formed by such an arrangement.

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