A179592 Decimal expansion of the circumradius of pentagonal cupola with edge length 1.

2, 2, 3, 2, 9, 5, 0, 5, 0, 9, 4, 1, 5, 6, 9, 0, 0, 4, 9, 5, 0, 0, 4, 1, 5, 3, 8, 3, 2, 4, 9, 6, 8, 2, 7, 7, 2, 9, 3, 4, 0, 8, 0, 7, 3, 0, 5, 7, 9, 1, 8, 1, 6, 4, 7, 4, 5, 7, 4, 4, 1, 2, 6, 0, 8, 2, 5, 5, 6, 5, 8, 9, 4, 9, 0, 1, 6, 4, 3, 8, 2, 8, 9, 6, 2, 4, 5, 1, 9, 5, 0, 6, 0, 9, 2, 7, 3, 7, 3, 8, 5, 6, 4, 7, 4

Offset

1,1

Comments

Pentagonal cupola: 15 vertices, 25 edges, and 12 faces.

Links

Table of n, a(n) for n=1..105.

Polytope Wiki, Pentagonal cupola.

Eric Weisstein's World of Mathematics, Pentagonal Cupola.

Wikipedia, Pentagonal cupola.

Wolfram Alpha, Johnson solid 5.

Index entries for algebraic numbers, degree 4.

Formula

Equals sqrt(11+4*sqrt(5))/2.

Minimal polynomial: 16*x^4 - 88*x^2 + 41. - Amiram Eldar, May 12 2026

Example

2.232950509415690049500415383249682772934080730579181647457441260...

Mathematica

RealDigits[N[Sqrt[11+4*Sqrt[5]]/2, 200]]

Crossrefs

Cf. A001622, A010527, A102208, A179290, A179292, A179294, A179449, A179450, A179451, A179452, A179552, A179553, A019881, A179587, A179588, A179589, A179590, A179591.

Sequence in context: A016001 A016012 A069138 * A384805 A058671 A016002

Adjacent sequences: A179589 A179590 A179591 * A179593 A179594 A179595

Keyword

nonn,cons,easy

Author

Vladimir Joseph Stephan Orlovsky, Jul 19 2010

Status

approved