excludes pairs of bicentric points such as the Brocard points (which are interchanged by a mirror-image reflection). As of 2020, the Encyclopedia of Triangle Centers lists over 39,000 different triangle centers. Tangential polygons and cyclic polygons A tangential polygon has each of its sides tangent to a particular circle, called the incircle or inscribed circle. The center of the incircle, called the incenter, can be considered a center of the polygon. A cyclic polygon has each of its vertices on a particular circle, called the circumcircle or circumscribed circle. The center of the circumcircle, called the circumcenter, can be considered a center of the polygon. If a polygon is both tangential and cyclic, it is called bicentric. (All triangles are bicentric, for example.) The incenter and circumcenter of a bicentric polygon are not in general the same point. General polygons The center of a general polygon can be defined in several different ways. The "vertex centroid" comes from considering the polygon as being empty but having equal masses at its vertices. The "side centroid" comes from considering the sides to have constant mass per unit length. The usual center, called just the centroid (center of area) comes from considering the surface of the polygon as having constant density. These three points are in general not all the same point. Projective conics In projective geometry every line has a point at infinity or "figurative point" where it crosses all the lines that are parallel to it. 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. The concept of center in projective geometry uses this relation. The following assertions are from G. B. Halsted. The harmonic conjugate of a point at infinity with respect to the end points of a finite sect is the 'center' of that sect. The pole of the straight at infinity with respect to a certain conic is the 'center' of the conic. The polar of any figurative point is on the center of the conic and is called a 'diameter'. The center of any ellipse is within it, for its polar does not meet the curve, and so there are no tangents from it to the