A378352 Decimal expansion of the volume of a (small) triakis octahedron with unit shorter edge length.

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

Offset

1,1

Comments

The (small) triakis octahedron is the dual polyhedron of the truncated cube.

Links

Table of n, a(n) for n=1..90.

Polytope Wiki, Triakis octahedron.

Eric Weisstein's World of Mathematics, Small Triakis Octahedron.

Wikipedia, Triakis octahedron.

Index entries for algebraic numbers, degree 2.

Formula

Equals sqrt(2) + 3/2 = A002193 + 3/2.

Equals A156035/2. - Hugo Pfoertner, Nov 24 2024

Minimal polynomial: 4*x^2 - 12*x + 1. - Amiram Eldar, Jun 09 2026

Example

2.9142135623730950488016887242096980785696718753769...

Mathematica

First[RealDigits[Sqrt[2] + 3/2, 10, 100]]
(* Alternative: *)
First[RealDigits[PolyhedronData["TriakisOctahedron", "Volume"], 10, 100]]

Crossrefs

Cf. A378351 (surface area), A378353 (inradius), A201488 (midradius), A378354 (dihedral angle).

Cf. A377299 (volume of a truncated cube with unit edge).

Cf. A156035.

Essentially the same as A002193 and A188582.

Sequence in context: A173995 A389314 A272868 * A074950 A388798 A346170

Adjacent sequences: A378349 A378350 A378351 * A378353 A378354 A378355

Keyword

nonn,cons,easy

Author

Paolo Xausa, Nov 23 2024

Status

approved