Geodesic
A Specialised Net of Quadrics Having Selfpolar Polyhedra, with Details of the Fivedimensional Example
Canadian journal of mathematics, Tome 33 (1981) no. 4, pp. 885-892

Voir la notice de l'article provenant de la source Cambridge University Press

If x 0,x 1, ... x n 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 η j , 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. 
Edge, W. L. A Specialised Net of Quadrics Having Selfpolar Polyhedra, with Details of the Fivedimensional Example. Canadian journal of mathematics, Tome 33 (1981) no. 4, pp. 885-892. doi: 10.4153/CJM-1981-069-3
@article{10_4153_CJM_1981_069_3,
     author = {Edge, W. L.},
     title = {A {Specialised} {Net} of {Quadrics} {Having} {Selfpolar} {Polyhedra,} with {Details} of the {Fivedimensional} {Example}},
     journal = {Canadian journal of mathematics},
     pages = {885--892},
     year = {1981},
     volume = {33},
     number = {4},
     doi = {10.4153/CJM-1981-069-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1981-069-3/}
}
TY  - JOUR
AU  - Edge, W. L.
TI  - A Specialised Net of Quadrics Having Selfpolar Polyhedra, with Details of the Fivedimensional Example
JO  - Canadian journal of mathematics
PY  - 1981
SP  - 885
EP  - 892
VL  - 33
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1981-069-3/
DO  - 10.4153/CJM-1981-069-3
ID  - 10_4153_CJM_1981_069_3
ER  - 
%0 Journal Article
%A Edge, W. L.
%T A Specialised Net of Quadrics Having Selfpolar Polyhedra, with Details of the Fivedimensional Example
%J Canadian journal of mathematics
%D 1981
%P 885-892
%V 33
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1981-069-3/
%R 10.4153/CJM-1981-069-3
%F 10_4153_CJM_1981_069_3

[1] 1. Baker, H. F., Principles of geometry, Vol. VI (Cambridge, 1933). Google Scholar

[2] 2. Bertini, E., Introduzione alia geometria proiettiva degli iperspazi (Messina, 1923). Google Scholar

[3] 3. Edge, W. L., A special net of quadrics, Proc. Edinburgh Math. Soc. (2) 4 (1936), 185–209. Google Scholar

[4] 4. Edge, W. L., Notes on a net of quadric surfaces V: The pentahedral net, Proc. London Math. . Soc. (2) 47 (1942), 455–480. Google Scholar

[5] 5. Edge, W. L., A special polyhedral net of quadrics, Journal London Math. Soc. (2) 22 (1980), 46–56. Google Scholar

Cité par Sources :