A378354 Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a (small) triakis octahedron.

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

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.

Wikipedia, Triakis octahedron.

Formula

Equals arccos(-(3 + 8*sqrt(2))/17) = arccos(-(3 + A377342)/17).

Example

2.57174440034566846791285405092806379355115694111...

Mathematica

First[RealDigits[ArcCos[-(3 + 8*Sqrt[2])/17], 10, 100]] (* or *)
First[RealDigits[First[PolyhedronData["TriakisOctahedron", "DihedralAngles"]], 10, 100]]

Crossrefs

Cf. A378351 (surface area), A378352 (volume), A378353 (inradius), A201488 (midradius).

Cf. A019669 and A195698 (dihedral angles of a truncated cube).

Cf. A377342.

Sequence in context: A181583 A010589 A024715 * A296479 A354088 A024709

Adjacent sequences: A378351 A378352 A378353 * A378355 A378357 A378358

Keyword

nonn,cons,easy,new

Author

Paolo Xausa, Nov 24 2024

Status

approved