Incenter centers known to the ancient Greeks, and the only one that does not in general lie on the Euler line. It is the first listed center, X(1), in Clark Kimberling's Encyclopedia of Triangle Centers, and the identity element of the multiplicative group of triangle centers. For polygons with more than three sides, the incenter only exists for tangential polygons—those that have an incircle that is tangent to each side of the polygon. In this case the incenter is the center of this circle and is equally distant from all sides. It is a theorem in Euclidean geometry that the three
Triangulation (geometry) to triangles. In particular, a pseudotriangulation of a point set is a partition of the convex hull of the points into pseudotriangles, polygons that like triangles have exactly three convex vertices. As in point set triangulations, pseudotriangulations are required to have their vertices at the given input points. Triangulation (geometry) In geometry, a triangulation is a subdivision of a planar object into triangles, and by extension the subdivision of a higher-dimension geometric object into simplices. Triangulations of a three-dimensional volume would involve subdividing it into tetrahedra ("pyramids" of various shapes and sizes) packed together. In most instances, the triangles of