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Special pairs of semi-bilogic and bilogic tetrahedra

Part of: Linear incidence geometry Geometry

Published online by Cambridge University Press:  09 April 2009

Sahib Ram Mandan
Sahib Ram Mandan
Affiliation:
Flat 19, “Vijaya”, Chhedanagar, Bombay-400089., India
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Abstract

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Let (A), (B) be a special pair of perspective tetrahedra such that the 4 joins of their corresponding vertices are perpendicular to their plane of perspectivity. It has been already established (Mandan (1977a), p. 573) that they are, in general, skew-orthologic such that the perpendiculars from the vertices of one to the corresponding opposite faces of the other lie in a regulus. Here we give a construction of a special pair of semi-orthologic and orthologic tetrahedra, the said regulus degenerating into 2 pairs of intersecting lines and 4 concurrent lines respectively. Following Thébault ((1952), p. 25; (1955), p. 67), we call them semi-bilogic and bilogic respectively.

MSC classification

Secondary: 51A20: Configuration theorems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 3 , November 1979 , pp. 303 - 308
Copyright
Copyright © Australian Mathematical Society 1979

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