OEIS A000944 · polyhedra with n vertices

Polyhedra Sampler

A polyhedron's skeleton is a 3-connected planar graph (Steinitz), so A000944 counts them: 1, 2, 7, 34, 257, 2606, 32300, … for n = 4, 5, 6, … (the OEIS lists n ≤ 18; the counts here for n = 19 to 40 are new, by formula). Each row below is a random sample of distinct polyhedra with n vertices, drawn in canonical form (every edge tangent to the unit sphere, so symmetric graphs look symmetric). Hover or tap one to mark its relatives in the sample.

One colour scale for both Faces are coloured by their number of sides, corners by their degree, and each half of an edge by the corner it leaves. Duality swaps the two, so a polyhedron and its dual trade colours between faces and corners.