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

Author

Paolo Xausa, Nov 30 2024

Keywords

• nonn
• cons
• easy

Comments

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

Examples

			2.410613141653407606153665785465949185980362906...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Wikipedia, Deltoidal icositetrahedron.
• Index entries for transcendental numbers.

Crossrefs

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

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

Programs

Mathematica

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

PARI

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

Formula

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

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