View source for Isogons and isohedra

Convex three-dimensional polyhedra (cf. [[Polyhedron|Polyhedron]]) whose polyhedral angles are equal (isogons), or all faces of which are the same (isohedra); the group of rotations (with reflections) of an isogon (isohedron) about the centre of gravity takes any vertex (face) to any other vertex (face). To each isogon corresponds a dual isohedron, and conversely. If a convex polyhedron is an isogon and an isohedron, then it is a regular polyhedron. There are 13 special cases and two infinite series of combinatorially-different isogons, which can be realized as [[Semi-regular polyhedra|semi-regular polyhedra]].



====Comments====
The 13 special isogons are called Archimedean solids, and their duals Catalan solids. Some of them play a role in the geometry of numbers and crystallography. For non-convex isogons and isohedra see [[#References|[a2]]].

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  L. Féjes Toth,   "Reguläre Figuren" , Ungar. Akad. Wissenschaft.  (1965)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  B. Grünbaum,   G. Shephard,   "Polyhedra with transitivity properties"  ''C.R. Math. Rep. Acad. Sci. Canada'' , '''6'''  (1984)  pp. 61–66</TD></TR></table>