A397163 Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a canonical (dual-uniform) tetragonal trapezohedron.

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

Offset

1,2

Comments

The tetragonal trapezohedron is the dual polyhedron of the square antiprism.

Links

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

David I. McCooey, Tetragonal Trapezohedron.

Polytope Wiki, Square antitegum.

Eric Weisstein's World of Mathematics, Trapezohedron.

Wikipedia, Tetragonal trapezohedron.

Index entries for transcendental numbers.

Formula

Equals arcsec(-1 - sqrt(8)) = arcsec(-1 - A010466).

Equals arccos((1 - sqrt(8))/7) = arccos((1 - A010466)/7).

Equals arccos(c), where c = -0.26120... is the smallest root of 7*x^2 - 2*x - 1.

Example

1.835065491872355962928478692680808140034308009175...

Mathematica

First[RealDigits[ArcSec[-1 - Sqrt[8]], 10, 100]]
(* Alternative: *)
First[RealDigits[First[PolyhedronData[{"Trapezohedron", 4}, "DihedralAngles"]], 10, 100]]

Prog

(PARI) acos((1-sqrt(8))/7) \\ Charles R Greathouse IV, Jul 06 2026

Crossrefs

Cf. A397156 (volume), A397157 (surface area), A397158 (inradius), A397159 (midradius), A397160 (height).

Cf. A397161 (small face angle), A397162 (large face angle).

Cf. A387149 and A387150 (dihedral angles of the dual).

Cf. A010466.

Sequence in context: A202779 A328498 A199440 * A199293 A357108 A110234

Adjacent sequences: A397160 A397161 A397162 * A397164 A397165 A397166

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jun 25 2026

Status

approved