A179552 Decimal expansion of the volume of pentagonal pyramid with edge length 1.

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

Offset

0,1

Comments

Pentagonal pyramid: 6 faces, 6 vertices, and 10 edges.

Also equals the covariance-matrix eigenvalue of the regular icosahedron with unit edge lengths. - Chittaranjan Pardeshi, Jul 18 2025

Links

Table of n, a(n) for n=0..104.

Polytope Wiki, Pentagonal pyramid.

Eric Weisstein's World of Mathematics, Pentagonal Pyramid.

Wikipedia, Covariance matrix.

Wikipedia, Pentagonal pyramid.

Wikipedia, Regular icosahedron.

Wolfram Alpha, Johnson solid 2.

Index entries for algebraic numbers, degree 2.

Formula

Equals (5+sqrt(5))/24.

Minimal polynomial: 144*x^2 - 60*x + 5. - Amiram Eldar, May 12 2026

Example

0.3015028323958245706837155695304698431433590983171469051779540518921...

Mathematica

RealDigits[N[(5+Sqrt[5])/24, 200]]

Prog

(PARI) (5+sqrt(5))/24 \\ Charles R Greathouse IV, Oct 30 2023

Crossrefs

Cf. A001622, A010527, A102208, A179290, A179292, A179294, A179449, A179450, A179451, A179452.

Sequence in context: A207543 A191532 A333852 * A119879 A115714 A346242

Adjacent sequences: A179549 A179550 A179551 * A179553 A179554 A179555

Keyword

nonn,cons,easy

Author

Vladimir Joseph Stephan Orlovsky, Jul 19 2010

Status

approved