A378394 Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a deltoidal icositetrahedron.

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

Offset

1,1

Comments

The deltoidal icositetrahedron is the dual polyhedron of the (small) rhombicuboctahedron.

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Wikipedia, Deltoidal icositetrahedron.

Index entries for transcendental numbers.

Formula

Equals arcsec(4*sqrt(2) - 7) = arcsec(A010487 - 7).

Equals arccos(-(4*sqrt(2) + 7)/17) = arccos(-(A010487 + 7)/17).

Example

2.410613141653407606153665785465949185980362906...

Mathematica

First[RealDigits[ArcSec[Sqrt[32] - 7], 10, 100]] (* or *)
First[RealDigits[First[PolyhedronData["DeltoidalIcositetrahedron", "DihedralAngles"]], 10, 100]]

Prog

(PARI) acos(-(4*sqrt(2) + 7)/17) \\ Charles R Greathouse IV, Feb 11 2025

Crossrefs

Cf. A378390 (surface area), A378391 (volume), A378392 (inradius), A378393 (midradius).

Cf. A177870 and A195702 (dihedral angles of a (small) rhombicuboctahedron).

Sequence in context: A164268 A294390 A152433 * A094344 A211183 A390670

Adjacent sequences: A378391 A378392 A378393 * A378395 A378396 A378397

Keyword

nonn,cons,easy

Author

Paolo Xausa, Nov 30 2024

Status

approved