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

Author

Paolo Xausa, Jun 11 2025

Keywords

• nonn
• cons
• easy

Comments

The pentagonal orthocupolarotunda is Johnson solid J_32.

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

Examples

			9.2418082864578952008524451431901588238346215825240...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Wikipedia, Pentagonal gyrocupolarotunda.
• Wikipedia, Pentagonal orthocupolarotunda.

Crossrefs

Cf. A384872 (surface area).

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

Programs

Mathematica

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

Formula

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

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