A395170 Decimal expansion of the largest dihedral angle, in radians, in a uniform 9-gonal antiprism.

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

Offset

1,1

Comments

This is the dihedral angle between triangular faces.

Links

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

Polytope Wiki, Enneagonal antiprism.

Eric Weisstein's World of Mathematics, Antiprism.

Wikipedia, Antiprism.

Index entries for transcendental numbers.

Formula

Equals arccos((1 - 4*cos(Pi/9))/3) = arccos((1 - 4*A019879)/3).

Equals arccos(c), where c = -0.91959... is the smallest root of 27*(x^3 - x^2 - x) + 19.

Example

2.7378323668609414026808339410125045234685361092460...

Mathematica

First[RealDigits[ArcCos[(1 - 4*Cos[Pi/9])/3], 10, 100]]
(* Alternative: *)
First[RealDigits[Max[PolyhedronData["NonagonalAntiprism", "DihedralAngles"]], 10, 100]]

Prog

(PARI) acos((1 - 4*cos(Pi/9))/3) \\ Charles R Greathouse IV, May 13 2026

Crossrefs

Cf. A395169 (the other dihedral angle).

Cf. A395164 (volume), A395165 (surface area), A395166 (midradius), A395167 (circumradius), A395168 (height).

Cf. A019879.

Sequence in context: A198388 A334375 A011304 * A196392 A021789 A348721

Adjacent sequences: A395167 A395168 A395169 * A395171 A395172 A395173

Keyword

nonn,cons,easy

Author

Paolo Xausa, Apr 30 2026

Status

approved