A384286 Decimal expansion of the surface area of a gyroelongated pentagonal rotunda with unit edge.

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

Offset: 2

Author

Paolo Xausa, May 30 2025

Keywords

• nonn
• cons
• easy

Comments

The gyroelongated pentagonal rotunda is Johnson solid J_25.

Examples

			31.00745430323851474443564586571797490853203978248...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 2..10000
• Wikipedia, Gyroelongated pentagonal rotunda.

Crossrefs

Cf. A384285 (volume).

Cf. A002163, A002194, A179553, A179591, A179640, A384141, A384284.

Programs

Mathematica

First[RealDigits[(15*Sqrt[3] + Sqrt[650 + 290*Sqrt[5]])/2, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J25", "SurfaceArea"], 10, 100]]

Formula

Equals (15*sqrt(3) + sqrt(650 + 290*sqrt(5)))/2 = (15*A002194 + sqrt(650 + 290*A002163))/2.

Equals the largest root of 256*x^8 - 339200*x^6 + 98924000*x^4 - 9264250000*x^2 + 176295015625.