QLP5: Clawson Center
This point was mentioned by J.W. Clawson. In his document at Ref31 this point is referred to as the “Orthic Center” of the Circumcenter Quadrangle.
The Circumcenter Quadrangle is defined by the circumcenters O1, O2, O3, O4 of the 4 component triangles Li.Lj.Lk of the Reference Quadrilateral L1.L2.L3.L4. These 4 circumcenters are concyclic on the Miquel Circle. The Orthocenters H1, H2, H3, H4 of the Component Triangles Oi.Oj.Ok of the Circumcenter Quadrangle O1.O2.O3.O4 again are concyclic (on the Hervey Circle with circumcenter QLP3 the KantorHervey Point).
Now QLP5 is the common midpoint of Oi.Hi (i=1,2,3,4).
Since Quadrangles O1.O2.O3.O4 and H1.H2.H3.H4 are homothetic it also can be said that QLP5 is the center of homothecy of Quadrangles O1.O2.O3.O4 and H1.H2.H3.H4.
Coordinates:
1st CTcoordinate:
l (m  n) (a^{2} S_{A} l + b^{2} S_{B} m + c^{2} S_{C} n + 8 Δ^{2} (m n  l m  l n) / l)
1st DTcoordinate:
(m^{2}n^{2}) (+Sa^{2} (m^{2}n^{2})^{2} + Sb^{2} (l^{2}n^{2})^{2} +Sc^{2} (l^{2}m^{2})^{2}
+2 (Sb Sc l^{4}+Sa Sc m^{4}+Sa Sb n^{4}) + 2 S^{2}(l^{2} (m^{2}+n^{2})3 m^{2} n^{2}))
Properties:
 QLP5 lies on these lines:
 QLP5 is the Reflection of QLP4 in QLP6.
 QLP5 is the Reflection of QLP20 in QLP22.
 The distance ratios between points QLP20, QLP22, QLP12, QLP5 are 3 : 1 : 2.
 QLP5 is the shared EulerPoncelet Point (QAP2) from the Circumcenter Quadrangle and from the Orthocenter Quadrangle in the Circumcenter Quadrangle (resp. O1.O2.O3.O4 and H1.H2.H3.H4 in picture QLP3).
 d(QLP5 , QLP12) = d(QLP2 , QLP3) / 3 (d = distance)
 QLP5 = Anticenter (see Ref13) of the (concyclic) circumcenters of the 4 component triangles of the Reference Quadrilateral O1.O2.O3.O4 (note Randy Hutson).
 QLP5 = Anticenter (see Ref13) of the (concyclic) orthocenters H1.H2.H3.H4 of 4 component triangles of above Quadrangle O1.O2.O3.O4 (note Randy Hutson).
 The 3 QAversions of QLP5 are collinear on a line parallel to QAL4 (note Eckart Schmidt).

QLP5 is the common point of the 4 Simson lines of Oi wrt Triangle Oj.Ok.Ol, where (i,j,k,l) ∈ (1,2,3,4) and O1, O2, O3, O4 are the 4 Circumcenters of the Component Triangles of the Reference Quadrangle (Seiichi Kirikami, August, 2012).
 The QAOrthopole(QATf3) of QLCi5 is a circle through QLP5.
 Let X3i (i=1,2,3,4) be the circumcenters of the triangles (Lj,Lk,Ll), where j,k,l=different numbers from (1,2,3,4) unequal i. Let L3i be the lines through X3i parallel to Li. QLP5 is the Homothetic Center of the Reference Quadrilateral and (L31,L32, L33, L34). This construction is similar to the construction of QLP20 and QLP22.