A385264 Decimal expansion of the volume of a gyroelongated pentagonal birotunda with unit edge.

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

Offset

2,1

Comments

The gyroelongated pentagonal birotunda is Johnson solid J_48.

Links

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

Wikipedia, Gyroelongated pentagonal birotunda.

Formula

Equals (45 + 17*sqrt(5) + 5*sqrt(2*(sqrt(650 + 290*sqrt(5)) - sqrt(5) - 1)))/6 = (45 + 17*A002163 + 5*sqrt(2*(sqrt(650 + 290*A002163) - A002163 - 1)))/6.

Equals the largest real root of 6561*x^8 - 393660*x^7 + 9316620*x^6 - 108207900*x^5 + 601832025*x^4 - 1417189500*x^3 + 965841750*x^2 + 597667500*x - 668786875.

Example

20.5848138117963990020365269299359278989411403764...

Mathematica

First[RealDigits[(45 + 17*# + 5*Sqrt[2*(Sqrt[650 + 290*#] - # - 1)])/6 & [Sqrt[5]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J48", "Volume"], 10, 100]]

Crossrefs

Cf. A385488 (surface area).

Cf. A002163, A384283, A385260, A385262.

Sequence in context: A173343 A334059 A133446 * A011122 A329960 A085009

Adjacent sequences: A385261 A385262 A385263 * A385265 A385266 A385267

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jun 30 2025

Status

approved