A386545 Decimal expansion of the surface area of a triaugmented truncated dodecahedron with unit edges.

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

Offset: 3

Author

Paolo Xausa, Jul 28 2025

Keywords

• nonn
• cons
• easy

Comments

The triaugmented truncated dodecahedron is Johnson solid J_71.

Examples

			104.56475635443777864447372938117268304912246671047...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 3..10000
• Wikipedia, Triaugmented truncated dodecahedron.

Crossrefs

Cf. A386544 (volume).

Cf. A002194, A010476, A377694, A385805, A386465, A386543.

Programs

Mathematica

First[RealDigits[(60 + 35*Sqrt[3] + 90*Sqrt[#] + 3*Sqrt[5*#])/4 & [5 + Sqrt[20]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J71", "SurfaceArea"], 10, 100]]

Formula

Equals (60 + 35*sqrt(3) + 90*sqrt(5 + 2*sqrt(5)) + 3*sqrt(5*(5 + 2*sqrt(5))))/4 = (60 + 35*A002194 + 90*sqrt(5 + A010476) + 3*sqrt(5*(5 + A010476)))/4.

Equals the largest root of 256*x^8 - 30720*x^7 - 1574400*x^6 + 238464000*x^5 + 68364000*x^4 - 390828240000*x^3 + 4437895162500*x^2 + 78660973125000*x - 1021409416546875.