A386691 Decimal expansion of the volume of a parabidiminished rhombicosidodecahedron with unit edges.

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

Offset: 2

Author

Paolo Xausa, Jul 30 2025

Keywords

• nonn
• cons
• easy

Comments

The parabidiminished rhombicosidodecahedron is Johnson solid J_80.

Also the volume of a metabidiminished rhombicosidodecahedron and a gyrate bidiminished rhombicosidodecahedron (Johnson solids J_81 and J_82, respectively) with unit edges.

Examples

			36.967233145831580803409780572760635295338486330...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 2..10000
• Wikipedia, Gyrate bidiminished rhombicosidodecahedron.
• Wikipedia, Metabidiminished rhombicosidodecahedron.
• Wikipedia, Parabidiminished rhombicosidodecahedron.

Crossrefs

Cf. A386692 (surface area).

Cf. A001622, A002163, A134946, A179590, A185093, A386689, A386693.

Programs

Mathematica

First[RealDigits[5/3*(11 + 5*Sqrt[5]), 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J80", "Volume"], 10, 100]]

Formula

Equals (5/3)*(11 + 5*sqrt(5)) = (5/3)*(11 + 5*A002163).

Equals A185093 - 2*A179590.

Equals (50/3)*A001622 + 10 = A134946*100 + 10.

Equals the largest root of 9*x^2 - 330*x - 100.