A386689 Decimal expansion of the volume of a diminished rhombicosidodecahedron with unit edges.

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

Offset

2,1

Comments

The diminished rhombicosidodecahedron is Johnson solid J_76.

Also the volume of a paragyrate diminished rhombicosidodecahedron, a metagyrate diminished rhombicosidodecahedron and a bigyrate diminished rhombicosidodecahedron (Johnson solids J_77, J_78 and J_79, respectively) with unit edges.

Links

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

Wikipedia, Bigyrate diminished rhombicosidodecahedron.

Wikipedia, Diminished rhombicosidodecahedron.

Wikipedia, Metagyrate diminished rhombicosidodecahedron.

Wikipedia, Paragyrate diminished rhombicosidodecahedron.

Formula

Equals 115/6 + 9*sqrt(5) = 115/6 + 9*A002163.

Equals A185093 - A179590.

Equals the largest root of 36*x^2 - 1380*x - 1355.

Example

39.29127846416477393434922968524815278563223190317...

Mathematica

First[RealDigits[115/6 + 9*Sqrt[5], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J76", "Volume"], 10, 100]]

Crossrefs

Cf. A386690 (surface area).

Cf. A002163, A179590, A185093, A386691, A386693.

Sequence in context: A354129 A060956 A125301 * A347214 A388929 A263559

Adjacent sequences: A386686 A386687 A386688 * A386690 A386691 A386692

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jul 29 2025

Status

approved