A386690 Decimal expansion of the surface area of a diminished rhombicosidodecahedron with unit edges.

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

Offset

2,1

Comments

The diminished rhombicosidodecahedron is Johnson solid J_76.

Also the surface area 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 25 + (15*sqrt(3) + 10*sqrt(5 + 2*sqrt(5)) + 11*sqrt(5*(5 + 2*sqrt(5))))/4 = 25 + (15*A002194 + 10*sqrt(5 + A010476) + 11*sqrt(5*(5 + A010476)))/4.

Equals the largest root of 256*x^8 - 51200*x^7 + 4070400*x^6 - 162560000*x^5 + 3311844000*x^4 - 27184400000*x^3 - 92251037500*x^2 + 2593051875000*x - 8774179671875.

Example

58.11465077780005950750278197201400152953339093...

Mathematica

First[RealDigits[25 + (15*Sqrt[3] + 10*Sqrt[#] + 11*Sqrt[5*#])/4 & [5 + Sqrt[20]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J76", "SurfaceArea"], 10, 100]]

Crossrefs

Cf. A386689 (volume).

Cf. A002194, A010476, A344149, A386692, A386694.

Sequence in context: A199073 A199069 A020797 * A199661 A343784 A377523

Adjacent sequences: A386687 A386688 A386689 * A386691 A386692 A386693

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jul 29 2025

Status

approved