A394071 Decimal expansion of the volume of a uniform heptagonal antiprism with unit edges.

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

Offset

1,1

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.

Formula

Equals (7/24)*(cot(Pi/7) + cot(Pi/14))*sqrt(4 - sec(Pi/14)^2) = (7/24)*(A178818 + cot(A019681))*sqrt(4 - sec(A019681)^2).

Equals the largest real root of 46656*x^6 - 508032*x^4 + 209916*x^2 + 2401.

Example

3.233915292855978877348368198023350486655463938323...

Mathematica

First[RealDigits[7*(Cot[Pi/7] + Cot[Pi/14])*Sqrt[4 - Sec[Pi/14]^2]/24, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["HeptagonalAntiprism", "Volume"], 10, 100]]

Crossrefs

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

Cf. A394076, A394077 (dihedral angles).

Cf. A019681, A178818.

Sequence in context: A323467 A341097 A239959 * A214435 A215926 A007888

Adjacent sequences: A394068 A394069 A394070 * A394072 A394073 A394074

Keyword

nonn,cons,easy

Author

Paolo Xausa, Mar 10 2026

Status

approved