Dihedral Angle - Dihedral Angles in Polyhedra

Dihedral Angles in Polyhedra

Every polyhedron, regular and irregular, convex and concave, has a dihedral angle at every edge.

A dihedral angle (also called the face angle) is the internal angle at which two adjacent faces meet. An angle of zero degrees means the face normal vectors are antiparallel and the faces overlap each other (Implying part of a degenerate polyhedron). An angle of 180 degrees means the faces are parallel (like a tiling). An angle greater than 180 exists on concave portions of a polyhedron.

Every dihedral angle in an edge-transitive polyhedron has the same value. This includes the 5 Platonic solids, the 4 Kepler–Poinsot polyhedra, the two quasiregular solids, and two quasiregular dual solids.