A181708 -id:A181708 - cp's OEIS frontend

A296603 Number of faces a Johnson solid can have.

5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 26, 27, 30, 32, 34, 37, 42, 47, 52, 62

Offset: 1

Jonathan Sondow, Jan 28 2018

Distinct terms in A242731, sorted.

n is a member if and only if A296604(n) > 0.

			The square pyramid is the Johnson solid with the fewest faces, namely, 5, so a(1) = 5.

Norman W. Johnson, Convex Polyhedra with Regular Faces, Canadian Journal of Mathematics, 18 (1966), 169-200.
Eric Weisstein's World of Mathematics, Johnson Solid.
Wikipedia, List of Johnson solids.
Victor A. Zalgaller, Convex Polyhedra with Regular Faces, Zap. Nauchn. Sem. LOMI, 1967, Volume 2. Pages 5-221 (Mi znsl1408).

Cf. A181708, A242731, A296602, A296604.

A296604 Number of Johnson solids with n faces.

Original entry on oeis.org

0, 0, 0, 0, 1, 2, 1, 4, 2, 4, 3, 4, 2, 8, 1, 3, 3, 4, 0, 6, 1, 4, 0, 2, 0, 4, 3, 0, 0, 1, 0, 5, 0, 1, 0, 0, 3, 0, 0, 0, 0, 7, 0, 0, 0, 0, 1, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0

Offset: 1

Jonathan Sondow, Jan 28 2018

nonn

Sum(n>0, a(n)) = 92, the number of Johnson solids, as conjectured by Johnson and proved by Zalgaller.

a(n) > 0 if and only if n is a member of A296603.

			The square pyramid is the only Johnson solid with five faces, so a(5) = 1.

Norman W. Johnson, Convex Polyhedra with Regular Faces, Canadian Journal of Mathematics, 18 (1966), 169-200.
Eric Weisstein's World of Mathematics, Johnson Solid.
Wikipedia, List of Johnson solids.
Victor A. Zalgaller, Convex Polyhedra with Regular Faces, Zap. Nauchn. Sem. LOMI, 1967, Volume 2. Pages 5-221 (Mi znsl1408).

Cf. A181708, A242731, A296602, A296603.

a(62) = 5.

a(n) = 0 for n > 62.

cp's OEIS Frontend

A296603 Number of faces a Johnson solid can have.

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