A179593 Decimal expansion of the volume of pentagonal rotunda with edge length 1.

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

Offset

1,1

Comments

Pentagonal rotunda: 20 vertices, 35 edges, and 17 faces.

Links

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

Polytope Wiki, Pentagonal rotunda.

Eric Weisstein's World of Mathematics, Pentagonal Rotunda.

Wikipedia, Pentagonal rotunda.

Wolfram Alpha, Johnson solid 6.

Index entries for algebraic numbers, degree 2.

Formula

Equals (45+17*sqrt(5))/12.

Minimal polynomial: 36*x^2 - 270*x + 145. - Amiram Eldar, May 18 2026

Example

6.91776296812470206991299603070264133354087600944966144271710443099823...

Mathematica

RealDigits[N[(45+17*Sqrt[5])/12, 200]]

Crossrefs

Cf. A001622, A010527, A102208, A179290, A179292, A179294, A179449, A179450, A179451, A179452, A179552, A179553, A019881, A179587, A179588, A179589, A179590, A179591, A179592.

Sequence in context: A275614 A198504 A357066 * A117871 A011454 A379105

Adjacent sequences: A179590 A179591 A179592 * A179594 A179595 A179596

Keyword

nonn,cons,easy

Author

Vladimir Joseph Stephan Orlovsky, Jul 19 2010

Status

approved