A384952 Decimal expansion of the volume of an elongated pentagonal orthobirotunda with unit edge.

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

Offset: 2

Author

Paolo Xausa, Jun 20 2025

Keywords

• nonn
• cons
• easy

Comments

The elongated pentagonal orthobirotunda is Johnson solid J_42.

Also the volume of an elongated pentagonal gyrobirotunda (Johnson solid J_43) with unit edge.

Examples

			21.52973477918753764625171850149755722709850737774...
		

Links

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

Crossrefs

Cf. A179451 (surface area - 10), A344149 (surface area + 20).

Cf. A002163, A010476, A384283, A384285, A384624, A384871, A384909, A384910.

Programs

Mathematica

First[RealDigits[(45 + 17*Sqrt[5] + 15*Sqrt[5 + Sqrt[20]])/6, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J42", "Volume"], 10, 100]]

Formula

Equals (45 + 17*sqrt(5) + 15*sqrt(5 + 2*sqrt(5)))/6 = (45 + 17*A002163 + 15*sqrt(5 + A010476))/6.

Equals the largest root of 1296*x^4 - 38880*x^3 + 252360*x^2 - 329400*x - 332975.