A385263 Decimal expansion of the surface area of a gyroelongated pentagonal cupolarotunda with unit edge.

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

Offset

2,1

Comments

The gyroelongated pentagonal cupolarotunda is Johnson solid J_47.

Links

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

Wikipedia, Gyroelongated pentagonal cupolarotunda.

Formula

Equals 5 + (35*sqrt(3) + 7*sqrt(25 + 10*sqrt(5)))/4 = 5 + (35*A002194 + 7*sqrt(25 + 10*A002163))/4.

Equals the largest root of 256*x^8 - 10240*x^7 - 134400*x^6 + 7616000*x^5 - 756000*x^4 - 1373680000*x^3 + 2724312500*x^2 + 55840875000*x - 106054671875.

Example

32.198786370350444777678239329896650406601165160912...

Mathematica

First[RealDigits[5 + (35*Sqrt[3] + 7*Sqrt[25 + 10*Sqrt[5]])/4, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J47", "SurfaceArea"], 10, 100]]

Crossrefs

Cf. A385262 (volume).

Cf. A002163, A002194, A384284, A385257, A385259, A385261.

Sequence in context: A108073 A057731 A126074 * A108916 A119421 A121581

Adjacent sequences: A385260 A385261 A385262 * A385264 A385265 A385266

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jun 30 2025

Status

approved