Isogonal figure

In geometry, a polytope (e.g. a polygon or polyhedron) or a tiling is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure.

The pseudorhombicuboctahedron – which is not isogonal – demonstrates that simply asserting that "all vertices look the same" is not as restrictive as the definition used here, which involves the group of isometries preserving the polyhedron or tiling.

All planar isogonal 2n-gons have dihedral symmetry (Dn, n = 2, 3, ...) with reflection lines across the mid-edge points.

Isogonal polyhedra and 2D tilings may be further classified: These definitions can be extended to higher-dimensional polytopes and tessellations.

A more restrictive term, k-uniform is defined as a k-isogonal figure constructed only from regular polygons.