A386694 Decimal expansion of the surface area of a tridiminished rhombicosidodecahedron with unit edges.

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

Offset

2,1

Comments

The tridiminished rhombicosidodecahedron is Johnson solid J_83.

Links

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

Wikipedia, Tridiminished rhombicosidodecahedron.

Formula

Equals (60 + 5*sqrt(3) + 30*sqrt(5 + 2*sqrt(5)) + 9*sqrt(5*(5 + 2*sqrt(5))))/4 = (60 + 5*A002194 + 30*sqrt(5 + A010476) + 9*sqrt(5*(5 + A010476)))/4.

Equals the largest root of 256*x^8 - 30720*x^7 + 844800*x^6 + 20736000*x^5 - 1109916000*x^4 + 6460560000*x^3 + 265641862500*x^2 - 4344667875000*x + 19010422828125.

Example

55.731986643576199441017595043656650533395140173888...

Mathematica

First[RealDigits[(60 + 5*Sqrt[3] + 30*Sqrt[#] + 9*Sqrt[5*#])/4 & [5 + Sqrt[20]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J83", "SurfaceArea"], 10, 100]]

Crossrefs

Cf. A386693 (volume).

Cf. A002194, A010476, A344149, A386690, A386692.

Sequence in context: A113272 A388829 A222392 * A049471 A049789 A234473

Adjacent sequences: A386691 A386692 A386693 * A386695 A386696 A386697

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jul 31 2025

Status

approved