A385260 Decimal expansion of the volume of a gyroelongated pentagonal bicupola with unit edge.

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

Offset

2,3

Comments

The gyroelongated pentagonal bicupola is Johnson solid J_46.

Links

Paolo Xausa, Table of n, a(n) for n = 2..10000

Wikipedia, Gyroelongated pentagonal bicupola.

Formula

Equals (10 + 8*sqrt(5) + 5*sqrt(2*(sqrt(650 + 290*sqrt(5)) - sqrt(5) - 1)))/6 = (10 + 8*A002163 + 5*sqrt(2*(sqrt(650 + 290*A002163) - A002163 - 1)))/6.

Equals the largest real root of 6561*x^8 - 87480*x^7 + 313470*x^6 + 753300*x^5 - 22424850*x^4 - 84591000*x^3 - 85909500*x^2 + 8715000*x + 35547500.

Example

11.397378512213381124089433093505680212446879503678...

Mathematica

First[RealDigits[(10 + 8*# + 5*Sqrt[2*(Sqrt[650 + 290*#] - # - 1)])/6 & [Sqrt[5]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J46", "Volume"], 10, 100]]

Crossrefs

Cf. A385261 (surface area).

Cf. A002163, A384283, A385256, A385258.

Sequence in context: A343786 A254158 A193026 * A296503 A388221 A265298

Adjacent sequences: A385257 A385258 A385259 * A385261 A385262 A385263

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jun 27 2025

Status

approved