A386464 Decimal expansion of the volume of an augmented truncated dodecahedron with unit edges.

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

Offset: 2

Author

Paolo Xausa, Jul 25 2025

Keywords

• nonn
• cons
• easy

Comments

The augmented truncated dodecahedron is Johnson solid J_68.

Examples

			87.3637098777040746856191001251416771010058551...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 2..10000
• Wikipedia, Augmented truncated dodecahedron.

Crossrefs

Cf. A386465 (surface area).

Cf. A179590, A204188, A377695, A386411, A386459, A386466, A386544.

Programs

Mathematica

First[RealDigits[505/12 + 81/4*Sqrt[5], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J68", "Volume"], 10, 100]]

Formula

Equals 505/12 + 81*sqrt(5)/4 = 505/12 + 81*A204188.

Equals A377695 + A179590.

Equals the largest root of 36*x^2 - 3030*x - 10055.