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

2,1

Comments

The pentagonal orthocupolarotunda is Johnson solid J_32.

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

Links

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

Wikipedia, Pentagonal gyrocupolarotunda.

Wikipedia, Pentagonal orthocupolarotunda.

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.

Example

23.538532332506058310041007622367288571887138891860...

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]]

Crossrefs

Cf. A384871 (volume).

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

Sequence in context: A161984 A337362 A125677 * A051358 A346248 A211245

Adjacent sequences: A384869 A384870 A384871 * A384873 A384874 A384875

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jun 11 2025

Status

approved