A384284 Decimal expansion of the surface area of a gyroelongated pentagonal cupola with unit edge.

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

Offset: 2

Author

Paolo Xausa, May 27 2025

Keywords

• nonn
• cons
• easy
• changed

Comments

The gyroelongated pentagonal cupola is Johnson solid J_24.

Examples

			25.240003790832583513731278051892586452816662365...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 2..10000
• Wikipedia, Gyroelongated pentagonal cupola.
• Index entries for algebraic numbers, degree 8

Crossrefs

Cf. A384283 (volume).

Cf. A002163, A002194, A179553, A179591, A179640, A384141.

Programs

Mathematica

First[RealDigits[(20 + 25*Sqrt[3] + Sqrt[725 + 310*Sqrt[5]])/4, 10, 100]]
First[RealDigits[PolyhedronData["J24", "SurfaceArea"], 10, 100]]

PARI

(20 + 25*sqrt(3) + sqrt(725 + 310*sqrt(5)))/4 \\ Charles R Greathouse IV, Aug 19 2025

Formula

Equals (20 + 25*sqrt(3) + sqrt(725 + 310*sqrt(5)))/4 = (20 + 25*A002194 + sqrt(725 + 310*A002163))/4.

Equals the largest root of 256*x^8 - 10240*x^7 + 12800*x^6 + 3200000*x^5 - 22476000*x^4 - 203280000*x^3 + 1412362500*x^2 + 3080375000*x - 17984046875.