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A pyramidal number of the form n(n+1)(4n-1)/6, The first few are 1, 7, 22, 50, 95, ... (OEIS A002412). The generating function of the hexagonal pyramidal numbers is ...

Johnson solid J_(57).

In hexagonal close packing, layers of spheres are packed so that spheres in alternating layers overlie one another. As in cubic close packing, each sphere is surrounded by 12 ...

A number which is simultaneously a heptagonal number Hep_n and hexagonal number Hex_m. Such numbers exist when 1/2n(5n-3)=m(2m-1). (1) Completing the square and rearranging ...

A number which is simultaneously a nonagonal number N_m and hexagonal number Hex_n and therefore satisfies the Diophantine equation 1/2m(7m-5)=n(2n-1). (1) Completing the ...

The dual of the great snub dodecicosidodecahedron and Wenninger dual W_(115).

The dual of the snub icosidodecadodecahedron U_(44) and Wenninger dual W_(112).

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

An undecahedron is a polyhedron having 11 faces. Examples include those illustrated above and summarized in the following table. F E V name 11 8 17 biaugmented triangular ...

A positive-height (outward-pointing) pyramid used in augmentation. The term was introduced by B. Grünbaum.