A385805 Decimal expansion of the surface area of a triaugmented dodecahedron with unit edge.

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

Offset: 2

Author

Paolo Xausa, Jul 09 2025

Keywords

• nonn
• cons
• easy

Comments

The triaugmented dodecahedron is Johnson solid J_61.

Examples

			21.97948713368399215555903157714450777070188723...
		

Links

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

Crossrefs

Cf. A385804 (volume).

Cf. A002194, A010476, A385696, A385803.

Programs

Mathematica

First[RealDigits[3/4*(5*Sqrt[3] + 3*Sqrt[25 + 10*Sqrt[5]]), 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J61", "SurfaceArea"], 10, 100]]

Formula

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

Equals the largest root of 256*x^8 - 172800*x^6 + 26244000*x^4 - 1230187500*x^2 + 8303765625.