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

Author

Paolo Xausa, Jun 05 2025

Keywords

• nonn
• cons
• easy

Comments

The pentagonal orthobicupola is Johnson solid J_30.

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

Examples

			17.771081820100127079336639808541900116171761474546...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 2..10000
• Wikipedia, Pentagonal orthobicupola.
• Wikipedia, Pentagonal gyrobicupola.

Crossrefs

Cf. A384624 (volume).

Cf. A002163, A384284, A384286, A384872.

Programs

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]]

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.