Isogonal Figure - 3 Dimensions: Isogonal Polyhedra

3 Dimensions: Isogonal Polyhedra

Isogonal polyhedra may be classified:

• Regular if it is also isohedral (face-transitive) and isotoxal (edge-transitive); this implies that every face is the same kind of regular polygon.
• Quasi-regular if it is also isotoxal (edge-transitive) but not isohedral (face-transitive).
• Semi-regular if every face is a regular polygon but it is not isohedral (face-transitive) or isotoxal (edge-transitive). (Definition varies among authors; e.g. some exclude solids with dihedral symmetry, or nonconvex solids.)
• Uniform if every face is a regular polygon, i.e. it is regular, quasiregular or semi-regular.
• Noble if it is also isohedral (face-transitive).

An isogonal polyhedron has a single kind of vertex figure. If the faces are regular (and the polyhedron is thus uniform) it can be represented by a vertex configuration notation sequencing the faces around each vertex.