Inscribed sphere

In the inscribed ball of a polyhedron is a sphere that touches all areas of the given polyhedron. The inscribed ball is next to the edge of the ball in space geometry, which is the inscribed circle of a polygon in the plane geometry.

The Center of the inscribed ball must have all of the interfaces of the same distance. He, therefore needs to be two limiting levels on all planes of symmetry ( bisecting planes). Since the intersection of these planes is generally empty, only special polyhedra have inscribed ball, especially all tetrahedron (not just the regular! ) And the five Platonic solids. Also, all the Catalan bodies have an inscribed ball, as their respective boundary surfaces all the same ( congruent ) are among themselves.