A384285 Decimal expansion of the volume of a gyroelongated pentagonal rotunda with unit edge.

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

Offset

2,2

Comments

The gyroelongated pentagonal rotunda is Johnson solid J_25.

Links

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

Wikipedia, Gyroelongated pentagonal rotunda.

Index entries for algebraic numbers, degree 8.

Formula

Equals (45 + 17*sqrt(5) + 10*sqrt(2*(sqrt(650 + 290*sqrt(5)) - sqrt(5) - 1)))/12 = (45 + 17*A002163 + 10*sqrt(2*(sqrt(650 + 290*A002163) - A002163 - 1)))/12.

Equals the largest real root of 1679616*x^8 - 50388480*x^7 + 603262080*x^6 - 3520972800*x^5 + 5215460400*x^4 + 4128624000*x^3 - 8894943000*x^2 + 3881385000*x - 424924375.

Example

13.667050843671696932123530899233286565400264...

Mathematica

First[RealDigits[(45 + 17*# + 10*Sqrt[2*(Sqrt[650 + 290*#] - # - 1)])/12 & [Sqrt[5]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J25", "Volume"], 10, 100]]

Crossrefs

Cf. A384286 (surface area).

Cf. A002163, A179590, A179639, A179641, A384138, A384140, A384144, A384213, A384283.

Sequence in context: A227501 A294981 A079093 * A153035 A296216 A072910

Adjacent sequences: A384282 A384283 A384284 * A384286 A384287 A384288

Keyword

nonn,cons,easy

Author

Paolo Xausa, May 29 2025

Status

approved