A384909 Decimal expansion of the volume of an elongated pentagonal orthobicupola with unit edge.

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

Offset: 2

Author

Paolo Xausa, Jun 12 2025

Keywords

• nonn
• cons
• easy

Comments

The elongated pentagonal orthobicupola is Johnson solid J_38.

Also the volume of an elongated pentagonal gyrobicupola (Johnson solid J_39) with unit edge.

Examples

			12.342299479604519768304624665067309540604246504993...
		

Links

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

Crossrefs

Cf. A384625 (surface area - 10).

Cf. A002163, A010476, A384283, A384624, A384871.

Programs

Mathematica

First[RealDigits[(10 + 8*Sqrt[5] + 15*Sqrt[5 + Sqrt[20]])/6, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J38", "Volume"], 10, 100]]

Formula

Equals (10 + 8*sqrt(5) + 15*sqrt(5 + 2*sqrt(5)))/6 = (10 + 8*A002163 + 15*sqrt(5 + A010476))/6.

Equals the largest root of 1296*x^4 - 8640*x^3 - 82440*x^2 - 109200*x + 76525.