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An S-Configuration in Euclidean and Elliptic n-space

Published online by Cambridge University Press:  20 November 2018

Ram Sahib Mandan*
Affiliation:
Indian Institute of Technology Kharagpur
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“The remarkable analogies which exist between the complete quadrilateral and the desmic system of points suggest that it may be possible to extend the properties considered above to spaces of higher dimensions”, remarks Prof. N. A. Court at the end of his paper (2). Here is an attempt in that direction in Euclidean as well as in elliptic 4-space, suggesting extensions in higher spaces. The corresponding figure, called an S-configuration, is discussed.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1958

References

1. Baker, H. F., Principles of geometry, vol. 4 (Cambridge, 1940), p. 104.Google Scholar
2. Court, N. A., Theorems, their converses and their extensions, Nat. Math. Mag., 17, 5 (1943), 1-7.Google Scholar
3. Coxeter, H. S. M.,Regular honeycombs in elliptic space, Proc. Lond. Math. Soc. (3), 4 (1954), 471-501.Google Scholar
4. Coxeter, H. S. M., The polytopes with regular-prismatic vertex figures, Phil. Trans. Royal Soc. A 229 (1931), 359–60.Google Scholar
5. Coxeter, H. S. M., Regular polytopes (London, 1948).Google Scholar
6. Mandan, Sahib Ram, Umbilical projection, Proc. Ind. Acad. Ses., Sec. A, 15, 1 (1942), 16-17.Google Scholar
7. Mandan, Sahib Ram, Harmonic inversion (in press).Google Scholar
8. Mandan, Sahib Ram, Altitudes of a simplex in four dimensional space (in press).Google Scholar
9 Mandan, Sahib Ram, Mutually selfpolar pentads in Si, Panjab Uni. Res. Bui., 14 (1951), 31-32.Google Scholar
10. Mandan, Sahib Ram, On four intersecting spheres (in press).Google Scholar