Centre (geometry)

So the centre of a square, rectangle, rhombus or parallelogram is where the diagonals intersect, this is (among other properties) the fixed point of rotational symmetries.

Similarly the centre of an ellipse or a hyperbola is where the axes intersect.

The incentre and circumcentre of a bicentric polygon are not in general the same point.

The "vertex centroid" comes from considering the polygon as being empty but having equal masses at its vertices.

The ellipse, parabola, and hyperbola of Euclidean geometry are called conics in projective geometry and may be constructed as Steiner conics from a projectivity that is not a perspectivity.

A symmetry of the projective plane with a given conic relates every point or pole to a line called its polar.