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Regular tessellations of the plane by two or more convex regular polygons such that the same polygons in the same order surround each polygon vertex are called semiregular ...

The augmented tridiminished icosahedron is Johnson solid J_(64), which is formed from augmentation of the triangular face adjecent to all three hexagons of the tridiminished ...

A theorem that classifies planar regular closed curves up to regular homotopy by their contour winding numbers (Whitney 1937). In his thesis, S. Smale generalized this result ...

A formula relating the number of polyhedron vertices V, faces F, and polyhedron edges E of a simply connected (i.e., genus 0) polyhedron (or polygon). It was discovered ...

The truncated dodecadodecahedral graph is the skeleton of the truncated dodecadodecahedron, which is the only uniform polyhedron for which this is the case. It will be ...

The dual polyhedron of the small ditrigonal dodecicosidodecahedron U_(43) and Wenninger dual W_(82).

The dual polyhedron of the small snub icosicosidodecahedron U_(32) and Wenninger dual W_(110).

The dual polyhedron of the small retrosnub icosicosidodecahedron and Wenninger dual W_(118).

A graph G is the edge graph of a polyhedron iff G is a simple planar graph which is 3-connected.

A quadrilateral, sometimes also known as a tetragon or quadrangle (Johnson 1929, p. 61) is a four-sided polygon. If not explicitly stated, all four polygon vertices are ...