A394077 Largest dihedral angle, in radians, in a uniform heptagonal antiprism.

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

Offset

1,1

Comments

This is the dihedral angle between triangular faces.

Links

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

David I. McCooey, Heptagonal Antiprism.

Polytope Wiki, Heptagonal antiprism.

Eric Weisstein's World of Mathematics, Antiprism.

Wikipedia, Antiprism.

Index entries for transcendental numbers.

Formula

Equals arccos((1 - 4*cos(Pi/7))/3) = arccos((1 - 4*A073052)/3).

Equals arccos(c), where c = -0.867958... is the smallest root of 27*x^3 - 9*x^2 - 27*x + 1.

Example

2.621873093429493958578568422819526896777753859808...

Mathematica

First[RealDigits[ArcCos[(1 - 4*Cos[Pi/7])/3], 10, 100]] (* or *)
First[RealDigits[Max[PolyhedronData["HeptagonalAntiprism", "DihedralAngles"]], 10, 100]]

Prog

(PARI) acos((1 - 4*cos(Pi/7))/3) \\ Charles R Greathouse IV, May 13 2026

Crossrefs

Cf. A394076 (the other dihedral angle).

Cf. A394071 (volume), A394072 (surface area), A394073 (midradius), A394074 (circumradius), A394075 (height).

Cf. A073052.

Sequence in context: A204935 A008905 A136760 * A303335 A332390 A289382

Adjacent sequences: A394074 A394075 A394076 * A394078 A394079 A394080

Keyword

nonn,cons,easy

Author

Paolo Xausa, Mar 21 2026

Status

approved