A384283 Decimal expansion of the volume of a gyroelongated pentagonal cupola with unit edge.

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

Offset

1,1

Comments

The gyroelongated pentagonal cupola is Johnson solid J_24.

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Wikipedia, Gyroelongated pentagonal cupola.

Index entries for algebraic numbers, degree 8

Formula

Equals (5 + 4*sqrt(5) + 5*sqrt(2*(sqrt(650 + 290*sqrt(5)) - sqrt(5) - 1)))/6 = (5 + A010532 + 5*sqrt(2*(sqrt(650 + 290*A002163) - A002163 - 1)))/6.

Equals the largest real root of 1679616*x^8 - 11197440*x^7 + 27060480*x^6 + 35769600*x^5 - 4456749600*x^4 - 10714248000*x^3 + 3828402000*x^2 + 13859430000*x + 5340175625.

Example

9.07333319388018799314998398101816272215313393060...

Mathematica

First[RealDigits[(5 + Sqrt[80] + 5*Sqrt[2*(Sqrt[650 + 290*Sqrt[5]] - Sqrt[5] - 1)])/6, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J24", "Volume"], 10, 100]]

Prog

(PARI) (5 + 4*sqrt(5) + 5*sqrt(2*(sqrt(650 + 290*sqrt(5)) - sqrt(5) - 1)))/6 \\ Charles R Greathouse IV, Aug 19 2025

Crossrefs

Cf. A384284 (surface area).

Cf. A002163, A010532, A179590, A179639, A179641, A384138, A384140, A384144, A384213.

Sequence in context: A363368 A097674 A388199 * A372830 A390151 A385960

Adjacent sequences: A384280 A384281 A384282 * A384284 A384285 A384286

Keyword

nonn,cons,easy

Author

Paolo Xausa, May 26 2025

Status

approved