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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).

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 ...

product_(k=1)^(infty)(1-x^k) = sum_(k=-infty)^(infty)(-1)^kx^(k(3k+1)/2) (1) = 1+sum_(k=1)^(infty)(-1)^k[x^(k(3k-1)/2)+x^(k(3k+1)/2)] (2) = (x)_infty (3) = ...

The pentagonal icositetrahedral graph is the Archimedean dual graph which is the skeleton of the pentagonal icositetrahedron. It is implemented in the Wolfram Language as ...

The pentagonal hexecontahedral graph is the Archimedean dual graph which is the skeleton of the pentagonal hexecontahedron. It is implemented in the Wolfram Language as ...

A pentagonal square triangular number is a number that is simultaneously a pentagonal number P_l, a square number S_m, and a triangular number T_n. This requires a solution ...