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

Author

Paolo Xausa, Jul 31 2025

Keywords

• nonn
• cons
• easy

Comments

The tridiminished rhombicosidodecahedron is Johnson solid J_83.

Examples

			55.731986643576199441017595043656650533395140173888...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 2..10000
• Wikipedia, Tridiminished rhombicosidodecahedron.

Crossrefs

Cf. A386693 (volume).

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

Programs

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]]

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.