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A Specialised Net of Quadrics Having Selfpolar Polyhedra, with Details of the Fivedimensional Example
Published online by Cambridge University Press: 20 November 2018
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If x0,x1, … xn are homogeneous coordinates in [n], projective space of n dimensions, the prime (to use the standard name for a hyperplane)
osculates, as θ varies, the rational normal curve C whose parametric form is [2, p. 347]
Take a set of n + 2 points on C for which θ = ηjζ where ζ is any complex number and
so that the ηj, for 0 ≦ j < n + 2, are the (n + 2)th roots of unity. The n + 2 primes osculating C at these points bound an (n + 2)-hedron H which varies with η, and H is polar for all the quadrics
(1.1)
in the sense that the polar of any vertex, common to n of its n + 2 bounding primes, contains the opposite [n + 2] common to the residual pair.
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- Research Article
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- Copyright © Canadian Mathematical Society 1981
References
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