QL-P18: Reflection of QL-P8 in QL-P12


QL-P18 is the Reflection of QL-P8 in QL-P12.
Special about this point is that it lies on QL-L9, the M3D Line. 
QL-P18-Reflection QL-P8 in QL-P12
Coordinates:
1st CT-coordinate:
       l3 (m - n)2 (m + n) - 2 l2 (m2 - n2)2 - 2 m2 n2 (m2 - m n + n2) + l m n (m + n) (4 m2 - 7 m n + 4 n2)
1st DT-coordinate:
       (m2-n2) (l2 (l2+m2+n2) - 3 m2n2) 
 
Properties:
        QL-P8.QL-P12   = QL-L8  (2 : -1 => P18 = Reflection of QL-P8 in QL-P12)
        QL-P18.QL-P23 = QL-L9
  • The 3 QA-versions of QL-P18 are collinear (note Eckart Schmidt).
  • QL-P18 is the centroid of the three collinear points QG-P15 on QL-L9 (Eckart Schmidt, October 9, 2013). See Ref-34, QFG #286 and #357.