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

2,1

Links

Table of n, a(n) for n=2..91.

Polytope Wiki, Truncated icosahedron.

Eric Weisstein's World of Mathematics, Truncated Icosahedron.

Wikipedia, Truncated icosahedron.

Index entries for algebraic numbers, degree 8.

Formula

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

Equals 30*(A002194 + A375067).

Minimal polynomial: x^8 - 11700*x^6 + 46392750*x^4 - 72945562500*x^2 + 37028746265625. - Amiram Eldar, May 17 2026

Example

72.60725303413392187893153397383948620117264765443...

Mathematica

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

Prog

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

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.

Sequence in context: A117029 A377276 A128475 * A387297 A309647 A225444

Adjacent sequences: A377747 A377748 A377749 * A377751 A377752 A377753

Keyword

nonn,cons,easy

Author

Paolo Xausa, Nov 06 2024

Status

approved