A384911 Decimal expansion of the surface area of an elongated pentagonal orthocupolarotunda with unit edge.

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

Offset: 2

Author

Paolo Xausa, Jun 13 2025

Keywords

• nonn
• cons
• easy

Comments

The elongated pentagonal orthocupolarotunda is Johnson solid J_40.

Also the surface area of an elongated pentagonal gyrocupolarotunda (Johnson solid J_41) with unit edge.

Examples

			33.538532332506058310041007622367288571887138891860...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 2..10000
• Wikipedia, Elongated pentagonal gyrocupolarotunda.
• Wikipedia, Elongated pentagonal orthocupolarotunda.

Crossrefs

Cf. A384910 (volume).

Cf. A002163, A384284, A384286, A384625.

Apart from the leading digit the same as A384872.

Programs

Mathematica

First[RealDigits[(60 + Sqrt[10*(190 + 49*Sqrt[5] + 21*Sqrt[75 + 30*Sqrt[5]])])/4, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J40", "SurfaceArea"], 10, 100]]

Formula

Equals (60 + sqrt(10*(190 + 49*sqrt(5) + 21*sqrt(75 + 30*sqrt(5)))))/4 = (60 + sqrt(10*(190 + 49*A002163 + 21*sqrt(75 + 30*A002163))))/4.

Equals the largest root of 256*x^8 - 30720*x^7 + 1491200*x^6 - 37440000*x^5 + 509444000*x^4 - 3437040000*x^3 + 5993612500*x^2 + 44939625000*x - 172099671875.