A386466 Decimal expansion of the volume of a parabiaugmented truncated dodecahedron with unit edges.

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

Offset: 2

Author

Paolo Xausa, Jul 25 2025

Keywords

• nonn
• cons
• easy

Comments

The parabiaugmented truncated dodecahedron is Johnson solid J_69.

Also the volume of a metabiaugmented truncated dodecahedron (Johnson solid J_70) with unit edges.

Examples

			89.68775519603726781655854923762919459129960068854...
		

Links

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

Crossrefs

Cf. A386543 (surface area).

Cf. A002163, A179590, A377695, A385578, A385802, A386464, A386544.

Programs

Mathematica

First[RealDigits[(515 + 251*Sqrt[5])/12, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J69", "Volume"], 10, 100]]

Formula

Equals (515 + 251*sqrt(5))/12 = (515 + 251*A002163)/12.

Equals A377695 + 2*A179590.

Equals the largest root of 36*x^2 - 3090*x - 12445.