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

Author

Paolo Xausa, Jul 29 2025

Keywords

• nonn
• cons
• easy

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.

Examples

			39.29127846416477393434922968524815278563223190317...
		

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.

Crossrefs

Cf. A386690 (surface area).

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

Programs

Mathematica

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

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.