A386003 Decimal expansion of the surface area of an augmented tridiminished icosahedron with unit edge.

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

Offset

1,1

Comments

The augmented tridiminished icosahedron is Johnson solid J_64.

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Wikipedia, Augmented tridiminished icosahedron.

Formula

Equals (7*sqrt(3) + 3*sqrt(5*(5 + 2*sqrt(5))))/4 = (7*A002194 + 3*sqrt(5*(5 + A010476)))/4.

Equals 3*A102771 + 7*A120011 = A386001 + 2*A120011.

Equals the largest root of 256*x^8 - 23808*x^6 + 484704*x^4 - 2752812*x^2 + 4626801.

Example

8.192521115012436031950067029801105440372031704...

Mathematica

First[RealDigits[(7*Sqrt[3] + 3*Sqrt[25 + 10*Sqrt[5]])/4, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J64", "SurfaceArea"], 10, 100]]

Crossrefs

Cf. A386002 (volume).

Cf. A002194, A010476, A102771, A120011, A386001.

Sequence in context: A230151 A308043 A286253 * A198674 A168321 A242047

Adjacent sequences: A386000 A386001 A386002 * A386004 A386005 A386006

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jul 18 2025

Status

approved