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The 60 Pascal lines of a hexagon inscribed in a conic section intersect three at a time through 20 Steiner points. There is a dual relationship between the 15 Plücker lines ...

The 60 Pascal lines of a hexagon inscribed in a conic intersect three at a time through 20 Steiner points, and also three at a time in 60 points known as Kirkman points. Each ...

A Kirkman triple system of order v=6n+3 is a Steiner triple system with parallelism (Ball and Coxeter 1987), i.e., one with the following additional stipulation: the set of ...

A coaxal system is a system of coaxal circles. A spectacular example is the set of circles (circumcircle, nine-point circle, orthocentroidal circle, orthoptic circle of the ...

The power of a fixed point A with respect to a circle of radius r and center O is defined by the product p=AP×AQ, (1) where P and Q are the intersections of a line through A ...

Two triangles DeltaA_1B_1C_1 and DeltaA_2B_2C_2 are orthologic if the perpendiculars from the vertices A_1, B_1, C_1 on the sides B_2C_2, A_2C_2, and A_2B_2 are concurrent. ...

The circumcircle is a triangle's circumscribed circle, i.e., the unique circle that passes through each of the triangle's three vertices. The center O of the circumcircle is ...

The point T at which the lines through the polygon vertices of a triangle perpendicular to the corresponding sides of the first Brocard triangle, are concurrent. The Tarry ...

A hexahedral graph is a polyhedral graph on six vertices. There are seven distinct hexahedral graphs (illustrated above) which, through duality, correspond to seven convex ...

A polyhedral graph on five nodes. There are two topologically distinct pentahedral graphs which, through duality, correspond to the skeletons of the square pyramid (left ...