A378351 Decimal expansion of the surface area of a (small) triakis octahedron with unit shorter edge length.

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

Offset

2,3

Comments

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

Links

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

Polytope Wiki, Triakis octahedron.

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

Wikipedia, Triakis octahedron.

Index entries for algebraic numbers, degree 4.

Formula

Equals 3*sqrt(7 + 4*sqrt(2)) = 3*sqrt(7 + A010487).

Minimal polynomial: x^4 - 126*x^2 + 1377. - Amiram Eldar, Jun 09 2026

Example

10.672941873983546705150008922490160564590104237715...

Mathematica

First[RealDigits[3*Sqrt[7 + Sqrt[32]], 10, 100]]
(* Alternative: *)
First[RealDigits[PolyhedronData["TriakisOctahedron", "SurfaceArea"], 10, 100]]

Crossrefs

Cf. A378352 (volume), A378353 (inradius), A201488 (midradius), A378354 (dihedral angle).

Cf. A377298 (surface area of a truncated cube with unit edge).

Cf. A010487.

Sequence in context: A395169 A316165 A267251 * A394042 A259526 A108664

Adjacent sequences: A378348 A378349 A378350 * A378352 A378353 A378354

Keyword

nonn,cons,easy

Author

Paolo Xausa, Nov 23 2024

Status

approved