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2t type a a,r type additional basis points arranged by fours basis point lies basis points arranged bitangent complete configuration complete table composed of planes cone of order congruence of Type conjugate congruences Conjugate Line double lines double point double quadric eight basis points equations family H family of quadrics focal surface four basis planes four basis points gruence Hence impose the condition imposing conditions k(x+y linear functions necessary and sufficient number of lines once a r line pair of singular pairs of planes parameters plane pencil planes and points planes and vertices planes of pencils planes pass points by fours possible to introduce quadric Q quadric surface quadrics of H quartic curve similar singular cone singular planes singular points six cones six planes six quadric cones Snyder sufficient condition symbol system of quadric table of planes twelve planes vertex vertices of pencils z+wX