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

2,1

Comments

The augmented dodecahedron is Johnson solid J_58.

Links

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

Wikipedia, Augmented dodecahedron.

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.

Example

21.090314915939732767258439678157046052159622437375...

Mathematica

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

Crossrefs

Cf. A385695 (volume).

Cf. A002194, A010476, A385803, A385805.

Sequence in context: A202817 A322222 A265012 * A285285 A374491 A338858

Adjacent sequences: A385693 A385694 A385695 * A385697 A385698 A385699

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jul 08 2025

Status

approved