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

2,1

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.

Links

Paolo Xausa, Table of n, a(n) for n = 2..10000

Wikipedia, Gyrate bidiminished rhombicosidodecahedron.

Wikipedia, Metabidiminished rhombicosidodecahedron.

Wikipedia, Parabidiminished rhombicosidodecahedron.

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.

Example

36.967233145831580803409780572760635295338486330...

Mathematica

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

Crossrefs

Cf. A386692 (surface area).

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

Sequence in context: A382236 A049341 A321943 * A351189 A187082 A377030

Adjacent sequences: A386688 A386689 A386690 * A386692 A386693 A386694

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jul 30 2025

Status

approved