A384871 Decimal expansion of the volume of a pentagonal orthocupolarotunda with unit edge.

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

Offset

1,1

Comments

The pentagonal orthocupolarotunda is Johnson solid J_32.

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

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Wikipedia, Pentagonal gyrocupolarotunda.

Wikipedia, Pentagonal orthocupolarotunda.

Formula

Equals (5/12)*(11 + 5*sqrt(5)) = (5/12)*(11 + 5*A002163).

Equals the largest root of 36*x^2 - 330*x - 25.

Example

9.2418082864578952008524451431901588238346215825240...

Mathematica

First[RealDigits[5*(11 + 5*Sqrt[5])/12, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J32", "Volume"], 10, 100]]

Crossrefs

Cf. A384872 (surface area).

Cf. A002163, A384144, A384283, A384285, A384624.

Sequence in context: A248320 A200282 A133841 * A388234 A099769 A176517

Adjacent sequences: A384868 A384869 A384870 * A384872 A384873 A384874

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jun 11 2025

Status

approved