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

A number which is simultaneously a nonagonal number N_m and pentagonal number P_n and therefore satisfies the Diophantine equation 1/2m(7m-5)=1/2n(3n-1). (1) Completing the ...

Johnson solid J_(16).

Johnson solid J_(41).

The dual of the great snub icosidodecahedron U_(57) and Wenninger dual W_(113).

Johnson solid J_(48).

Johnson solid J_(25).

The dual of the snub dodecadodecahedron U_(40) and Wenninger dual W_(111).

A centered polygonal number consisting of a central dot with five dots around it, and then additional dots in the gaps between adjacent dots. The general term is ...

A triacontahedron is a 30-faced polyhedron. Examples include the 14-gonal antiprism, biaugmented truncated cube (Johnson solid J_(67)), 15-gonal dipyramid, 28-gonal prism, ...