A385696 Decimal expansion of the surface area of an augmented dodecahedron with unit edge.

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

Offset: 2

Author

Paolo Xausa, Jul 08 2025

Keywords

• nonn
• cons
• easy

Comments

The augmented dodecahedron is Johnson solid J_58.

Examples

			21.090314915939732767258439678157046052159622437375...
		

Links

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

Crossrefs

Cf. A385695 (volume).

Cf. A002194, A010476, A385803, A385805.

Programs

Mathematica

First[RealDigits[(5*Sqrt[3] + 11*Sqrt[25 + 10*Sqrt[5]])/4, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J58", "SurfaceArea"], 10, 100]]

Formula

Equals (5*sqrt(3) + 11*sqrt(5*(5 + 2*sqrt(5))))/4 = (5*A002194 + 11*sqrt(5*(5 + A010476)))/4.

Equals the largest root of 256*x^8 - 198400*x^6 + 41204000*x^4 - 1620087500*x^2 + 7460640625.