A384625 Decimal expansion of the surface area of a pentagonal orthobicupola with unit edge.

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

Offset

2,2

Comments

The pentagonal orthobicupola is Johnson solid J_30.

Also the surface area of a pentagonal gyrobicupola (Johnson solid J_31) with unit edge.

Links

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

Wikipedia, Pentagonal orthobicupola.

Wikipedia, Pentagonal gyrobicupola.

Formula

Equals 10 + sqrt(5*(10 + sqrt(5) + sqrt(75 + 30*sqrt(5)))/2) = 10 + sqrt(5*(10 + A002163 + sqrt(75 + 30*A002163))/2).

Equals the largest root of x^8 - 80*x^7 + 2700*x^6 - 50000*x^5 + 552750*x^4 - 3710000*x^3 + 14628125*x^2 - 30562500*x + 25328125.

Example

17.771081820100127079336639808541900116171761474546...

Mathematica

First[RealDigits[10 + Sqrt[5*(10 + Sqrt[5] + Sqrt[75 + 30*Sqrt[5]])/2], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J30", "SurfaceArea"], 10, 100]]

Crossrefs

Cf. A384624 (volume).

Cf. A002163, A384284, A384286, A384872.

Sequence in context: A382587 A022619 A393899 * A131685 A019860 A011422

Adjacent sequences: A384622 A384623 A384624 * A384626 A384627 A384628

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jun 05 2025

Status

approved