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

1,1

Comments

The gyroelongated square bicupola is Johnson solid J_45.

Links

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

Wikipedia, Gyroelongated square bicupola.

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.

Example

8.1535748336212634025260213162662727026732149...

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]]

Crossrefs

Cf. A385259 (surface area).

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

Sequence in context: A338935 A393259 A200120 * A154861 A153495 A046471

Adjacent sequences: A385255 A385256 A385257 * A385259 A385260 A385261

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jun 26 2025

Status

approved