A179553 Decimal expansion of the surface area of pentagonal pyramid with edge length 1.

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

Offset

1,1

Comments

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

Links

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

Polytope Wiki, Pentagonal pyramid.

Eric Weisstein's World of Mathematics, Pentagonal Pyramid.

Wikipedia, Pentagonal pyramid.

Wolfram Alpha, Johnson solid 2.

Index entries for algebraic numbers, degree 8.

Formula

Equals sqrt(5/2*(10+sqrt(5)+sqrt(75+30sqrt(5))))/2.

Minimal polynomial: 256*x^8 - 6400*x^6 + 44000*x^4 - 87500*x^2 + 15625. - Amiram Eldar, May 12 2026

Example

3.885540910050063539668319904270950058085880737273174114276853431338785...

Mathematica

RealDigits[N[Sqrt[5/2*(10+Sqrt[5]+Sqrt[75+30*Sqrt[5]])]/2, 200]]

Crossrefs

Cf. A001622, A010527, A102208, A179290, A179292, A179294, A179449, A179450, A179451, A179452, A179552.

Sequence in context: A232182 A118817 A386736 * A384287 A157471 A288094

Adjacent sequences: A179550 A179551 A179552 * A179554 A179555 A179556

Keyword

nonn,cons,easy

Author

Vladimir Joseph Stephan Orlovsky, Jul 19 2010

Status

approved