A385258 Decimal expansion of the volume of a gyroelongated square bicupola with unit edge.

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

Offset: 1

Author

Paolo Xausa, Jun 26 2025

Keywords

• nonn
• cons
• easy

Comments

The gyroelongated square bicupola is Johnson solid J_45.

Examples

			8.1535748336212634025260213162662727026732149...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Wikipedia, Gyroelongated square bicupola.

Crossrefs

Cf. A385259 (surface area).

Cf. A002193, A010466, A179587, A384214, A384287, A385256.

Programs

Mathematica

First[RealDigits[2/3*(3 + 2*# + Sqrt[2*(2 + # + Sqrt[146 + 103*#])]) & [Sqrt[2]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J45", "Volume"], 10, 100]]

Formula

Equals (2/3)*(3 + 2*sqrt(2) + sqrt(2*(2 + sqrt(2) + sqrt(146 + 103*sqrt(2))))) = (2/3)*(3 + A010466 + sqrt(2*(2 + A002193 + sqrt(146 + 103*A002193)))).

Equals the largest real root of 6561*x^8 - 104976*x^7 + 594864*x^6 - 1384128*x^5 - 552096*x^4 + 1569024*x^3 + 246528*x^2 - 119808*x + 4352.