A386465 Decimal expansion of the surface area of an augmented truncated dodecahedron with unit edges.

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

Offset: 3

Author

Paolo Xausa, Jul 25 2025

Keywords

• nonn
• cons
• easy

Comments

The augmented truncated dodecahedron is Johnson solid J_68.

Examples

			102.18209222021391857798854245281533205298421595361...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 3..10000
• Wikipedia, Augmented truncated dodecahedron.

Crossrefs

Cf. A386464 (volume).

Cf. A002194, A010476, A377694, A386412, A386460, A386543, A386545.

Programs

Mathematica

First[RealDigits[(20 + 25*Sqrt[3] + 110*Sqrt[#] + Sqrt[5*#])/4 & [5 + Sqrt[20]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J68", "SurfaceArea"], 10, 100]]

Formula

Equals (20 + 25*sqrt(3) + 110*sqrt(5 + 2*sqrt(5)) + sqrt(5*(5 + 2*sqrt(5))))/4 = (20 + 25*A002194 + 110*sqrt(5 + A010476) + sqrt(5*(5 + A010476)))/4.

Equals the largest root of 256*x^8 - 10240*x^7 - 3955200*x^6 + 122240000*x^5 + 16152924000*x^4 - 343551280000*x^3 - 11461251137500*x^2 + 131995515375000*x + 634637481578125.