A179591 Decimal expansion of the surface area of pentagonal cupola with edge length 1.

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

Offset

2,2

Comments

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

Links

Table of n, a(n) for n=2..106.

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 8.

Formula

Equals (20+sqrt(10*(80+31*sqrt(5)+sqrt(2175+930*sqrt(5)))))/4.

Minimal polynomial: 256*x^8 - 10240*x^7 + 128000*x^6 - 256000*x^5 - 5556000*x^4 + 34320000*x^3 - 25837500*x^2 - 177625000*x + 229703125. - Amiram Eldar, May 12 2026

Example

16.5797497529881970460940463443632246181026360961176551818747440...

Mathematica

RealDigits[N[(20+Sqrt[10*(80+31*Sqrt[5]+Sqrt[2175+930*Sqrt[5]])])/4, 200]]

Crossrefs

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

Sequence in context: A191102 A021156 A182448 * A389265 A063046 A104909

Adjacent sequences: A179588 A179589 A179590 * A179592 A179593 A179594

Keyword

nonn,cons,easy

Author

Vladimir Joseph Stephan Orlovsky, Jul 19 2010

Status

approved