Bulletin of the Calcutta Mathematical Society December 1941

The section of this cubic by the plane B2C2D2 is the degenerate curve * consisting of the three lines C2D2 B2D2 B2C2 as the diagonal triangle of the 'quadrilateral formed by the lines common to the plane B2C2D2 and the faces of T1 is seen to be B2C2D2 and thence the lines C2D2 B2D2 B2C2 meet the pairs of edges of T1. [...] PROPERTIES OF MUTUALLY SELFPOLAR TETRAHEDRA 149 3. If Ti T3 be a pair of mutually selfpolar tetrahedra (a pair of skew edges of T1 then meets a pair of edges of T3) a second pair of skew edges of T1 meet a second pair of edges of T3 and the third pair of edges of Ti meet the third pair of edges of T3 and thence Ti i8 desmic with T. Let A‘B CiD be the tetrahedron To As Ti is selfpolar ti) T3 le [...] Then P1Q2 P2Qi the other common generators of the pairs of quadrics 121 C23 and 522 124 are the edges of a tetrahedron T„ while PI Q2 P2 Q1 the other common generators of the pairs of quadrics 522 t23 and OD 524 are edges of the other tetrahedron Li. [...] If from an arbitrary point Ai the transversal of a pair of opposite edges of a tetrahedron T is drawn and on this line is taken the fourth harmonic of Al w. r. t. the two points where the transversal meets the pair of opposite edges then the three such fourth harmonics corresponding to the three pairs of opposite edges of T constitute a plane called the polar plane of Al w. r. t. T.' [...] r. t. T of a point A1 does not only contain the points mentioned in the introduction but also the point which is the fourth harmonic of the point where the transversal from A1 to a pair of opposite edges meets one of the edges iv.