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

Author

Paolo Xausa, Jul 18 2025

Keywords

• nonn
• cons
• easy

Comments

The augmented tridiminished icosahedron is Johnson solid J_64.

Examples

			8.192521115012436031950067029801105440372031704...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Wikipedia, Augmented tridiminished icosahedron.

Crossrefs

Cf. A386002 (volume).

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

Programs

Mathematica

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

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.