A394076 Smallest dihedral angle, in radians, in a uniform heptagonal antiprism.

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

Offset

1,2

Comments

This is the dihedral angle between a triangular face and an heptagonal face.

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(-tan(Pi/14)/sqrt(3)) = arccos(-A020760*A343059).

Equals arccos((cot(Pi/7) - csc(Pi/7))/sqrt(3)) = arccos((A178818-A121598)/A002194).

Equals arccos(c), where c = -0.131776... is the third smallest real root of 189*x^6 - 315*x^4 + 63*x^2 - 1.

Example

1.7029571531467470730450715262481241152723726253334...

Mathematica

First[RealDigits[ArcCos[-Tan[Pi/14]/Sqrt[3]], 10, 100]] (* or *)
First[RealDigits[Min[PolyhedronData["HeptagonalAntiprism", "DihedralAngles"]], 10, 100]]

Prog

(PARI) acos(-tan(Pi/14)/sqrt(3)) \\ Charles R Greathouse IV, May 13 2026

Crossrefs

Cf. A394077 (the other dihedral angle).

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

Cf. A002194, A020760, A121598, A178818, A343059.

Sequence in context: A244979 A118288 A375191 * A094153 A243374 A309608

Adjacent sequences: A394073 A394074 A394075 * A394077 A394078 A394079

Keyword

nonn,cons,easy

Author

Paolo Xausa, Mar 19 2026

Status

approved