High Quality Content by WIKIPEDIA articles! In geometry, a polytope (a polygon, polyhedron or tiling, for example) is isogonal or vertex-transitive if, loosely speaking, all its vertices are the same. That implies that each vertex is surrounded by the same kinds of face in the same or reverse order, and with the same angles between corresponding faces. Technically, we say that for any two vertices there exists a symmetry of the polytope mapping the first isometrically onto the second. Other ways of saying this are that the polytope is transitive on its vertices, or that the vertices lie within a single symmetry orbit.

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