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

Author

Paolo Xausa, May 26 2025

Keywords

• nonn
• cons
• easy

Comments

The gyroelongated pentagonal cupola is Johnson solid J_24.

Examples

			9.07333319388018799314998398101816272215313393060...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Wikipedia, Gyroelongated pentagonal cupola.
• Index entries for algebraic numbers, degree 8

Crossrefs

Cf. A384284 (surface area).

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

Programs

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]]

PARI

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

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.