A384872 Decimal expansion of the surface area of a pentagonal orthocupolarotunda with unit edge.

2, 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 11 2025

Keywords

• nonn
• cons
• easy

Comments

The pentagonal orthocupolarotunda is Johnson solid J_32.

Also the surface area of a pentagonal gyrocupolarotunda (Johnson solid J_33) with unit edge.

Examples

			23.538532332506058310041007622367288571887138891860...
		

Links

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

Crossrefs

Cf. A384871 (volume).

Cf. A002163, A002194, A384284, A384286, A384625.

Programs

Mathematica

First[RealDigits[5 + 15/4*Sqrt[3] + 7/4*Sqrt[25 + 10*Sqrt[5]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J32", "SurfaceArea"], 10, 100]]

Formula

Equals 5 + (15/4)*sqrt(3) + (7/4)*sqrt(25 + 10*sqrt(5)) = 5 + (15/4)*A002194 + (7/4)*sqrt(25 + 10*A002163).

Equals the largest root of 256*x^8 - 10240*x^7 + 57600*x^6 + 1856000*x^5 - 21756000*x^4 + 6320000*x^3 + 484812500*x^2 - 364125000*x - 342171875.