A377750 Decimal expansion of the surface area of a truncated icosahedron with unit edge length.

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

Offset: 2

Author

Paolo Xausa, Nov 06 2024

Keywords

• nonn
• cons
• easy

Examples

			72.60725303413392187893153397383948620117264765443...
		

Links

• Eric Weisstein's World of Mathematics, Truncated Icosahedron.
• Wikipedia, Truncated icosahedron.
• Index entries for algebraic numbers, degree 8.

Crossrefs

Cf. A377751 (volume), A377752 (circumradius), A205769 (midradius + 1), A377787 (Dehn invariant).

Cf. A010527 (analogous for a regular icosahedron, with offset 1).

Cf. A002163, A002194, A375067.

Programs

Mathematica

First[RealDigits[3*(10*Sqrt[3] + Sqrt[25 + Sqrt[500]]), 10, 100]] (* or *)
First[RealDigits[PolyhedronData["TruncatedIcosahedron", "SurfaceArea"], 10, 100]]

PARI

3*(10*sqrt(3) + sqrt(25 + 10*sqrt(5))) \\ Charles R Greathouse IV, Feb 05 2025

Formula

Equals 3*(10*sqrt(3) + sqrt(25 + 10*sqrt(5))) = 30*A002194 + 3*sqrt(25 + 10*A002163).

Equals 30*(A002194 + A375067).