A378353 Decimal expansion of the inradius of a (small) triakis octahedron with unit shorter edge length.

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

Offset

0,1

Comments

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

Links

Table of n, a(n) for n=0..89.

Polytope Wiki, Triakis octahedron.

Eric Weisstein's World of Mathematics, SmallTriakisOctahedron.

Wikipedia, Triakis octahedron.

Index entries for algebraic numbers, degree 4.

Formula

Equals sqrt(23/68 + 4*sqrt(2)/17) = sqrt(23/68 + A010487/17).

Minimal polynomial: 272*x^4 - 184*x^2 + 1. - Amiram Eldar, Jun 09 2026

Example

0.81914066340325716171549134573565316624155520306132...

Mathematica

First[RealDigits[Sqrt[23/68 + Sqrt[32]/17], 10, 100]]
(* Alternative: *)
First[RealDigits[PolyhedronData["TriakisOctahedron", "Inradius"], 10, 100]]

Crossrefs

Cf. A378351 (surface area), A378352 (volume), A201488 (midradius), A378354 (dihedral angle).

Cf. A010487.

Sequence in context: A141228 A133820 A258718 * A019864 A230151 A308043

Adjacent sequences: A378350 A378351 A378352 * A378354 A378355 A378356

Keyword

nonn,cons,easy

Author

Paolo Xausa, Nov 23 2024

Status

approved