A377751 Decimal expansion of the volume of a truncated icosahedron with unit edge length.

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

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 2.

Formula

Equals (125 + 43*sqrt(5))/4 = (125 + 43*A002163)/4.

Minimal polynomial: 4*x^2 - 250*x + 1595. - Amiram Eldar, May 17 2026

Example

55.28773075812273923639861693886121953098664736582...

Mathematica

First[RealDigits[(125 + 43*Sqrt[5])/4, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["TruncatedIcosahedron", "Volume"], 10, 100]]

Prog

(PARI) (125 + 43*sqrt(5))/4 \\ Charles R Greathouse IV, Feb 05 2025

Crossrefs

Cf. A377750 (surface area), A377752 (circumradius), A205769 (midradius + 1), A377787 (Dehn invariant).

Cf. A102208 (analogous for a regular icosahedron).

Cf. A002163.

Sequence in context: A021648 A287746 A377804 * A128006 A157703 A332507

Adjacent sequences: A377748 A377749 A377750 * A377752 A377753 A377754

Keyword

nonn,cons,easy

Author

Paolo Xausa, Nov 07 2024

Status

approved