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.

Vertex-transitive is a synonym borrowed from modern ideas such as symmetry groups and graph theory.

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.

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