A306949 a(n) is the number of different types of faces of Johnson solid J_n, with solids ordered by indices in Johnson's paper.

2, 2, 3, 3, 4, 3, 2, 2, 3, 2, 2, 1, 1, 2, 2, 2, 1, 3, 3, 4, 4, 3, 3, 4, 3, 2, 2, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 2, 2, 2, 1, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 1, 2, 2, 2, 2, 2, 2, 3, 4

Offset

1,1

Comments

A299529(x) equals the number of times the value x occurs as a term in this sequence. In particular, if A299529(x) = 0, then x does not occur in this sequence.

References

V. A. Zalgaller, Convex Polyhedra with Regular Faces, in: Seminars in mathematics, Springer, 1969, ISBN 978-1-4899-5671-2.

Links

Table of n, a(n) for n=1..92.

N. W. Johnson, Convex Polyhedra with Regular Faces, Canadian Journal of Mathematics 18 (1966), 169-200.

Wikipedia, List of Johnson solids

V. A. Zalgaller, Convex Polyhedra with Regular Faces, Zapiski Nauchnykh Seminarov LOMI 2 (1967), 5-221.

Example

For n = 5: Johnson solid J_5 is the pentagonal cupola. This solid is bounded by 5 equilateral triangles, 5 squares, 1 pentagon and 1 decagon. Thus, there are 4 types of polygons making up the faces of this solid, hence a(5) = 4.

Crossrefs

Cf. A242731, A242732, A242733, A296603, A296604, A299529.

Sequence in context: A006546 A031268 A237817 * A189025 A236347 A045430

Adjacent sequences: A306946 A306947 A306948 * A306950 A306951 A306952

Keyword

nonn,fini,full

Author

Felix Fröhlich, Mar 17 2019

Extensions

a(68) corrected and a(88)-a(92) added by Pontus von Brömssen, Mar 13 2021

Status

approved