A385262 Decimal expansion of the volume of a gyroelongated pentagonal cupolarotunda with unit edge.

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

Offset: 2

Author

Paolo Xausa, Jun 27 2025

Keywords

• nonn
• cons
• easy

Comments

The gyroelongated pentagonal cupolarotunda is Johnson solid J_47.

Examples

			15.991096162004890063062980011720804055694009940053...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 2..10000
• Wikipedia, Gyroelongated pentagonal cupolarotunda.

Crossrefs

Cf. A385263 (surface area).

Cf. A002163, A384283, A385256, A385258, A385260.

Programs

Mathematica

First[RealDigits[5/12*(11 + 5*# + 2*Sqrt[2*(Sqrt[650 + 290*#] - # - 1)]) & [Sqrt[5]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J47", "Volume"], 10, 100]]

Formula

Equals (5/12)*(11 + 5*sqrt(5) + 2*sqrt(2*(sqrt(650 + 290*sqrt(5)) - sqrt(5) - 1))) = (5/12)*(11 + 5*A002163 + 2*sqrt(2*(sqrt(650 + 290*A002163) - A002163 - 1))).

Equals the largest real root of 1679616*x^8 - 61585920*x^7 + 851472000*x^6 - 5108832000*x^5 + 4745790000*x^4 + 21346200000*x^3 - 29019375000*x^2 - 4576875000*x - 405859375.