A394075 Decimal expansion of the height of a uniform heptagonal antiprism with unit edges.

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

Offset

0,1

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

David I. McCooey, Heptagonal Antiprism.

Polytope Wiki, Heptagonal antiprism.

Eric Weisstein's World of Mathematics, Antiprism.

Wikipedia, Antiprism.

Index entries for algebraic numbers, degree 6.

Formula

Equals sqrt(1 - (sec(Pi/14)^2)/4).

Equals sqrt((1 + 2*cos(Pi/7))/(2 + 2*cos(Pi/7))) = sqrt((1 + A160389)/(2 + A160389)).

Equals the largest real root of 7*x^6 - 7*x^4 + 1.

Example

0.85847319649455465240495522867191767826303596393848...

Mathematica

First[RealDigits[Sqrt[1 - (Sec[Pi/14]^2)/4], 10, 100]]

Prog

(PARI) sqrt(1 - 1/cos(Pi/14)^2/4) \\ Charles R Greathouse IV, May 13 2026

Crossrefs

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

Cf. A394076, A394077 (dihedral angles).

Cf. A160389.

Sequence in context: A119812 A153799 A086235 * A157742 A200134 A021542

Adjacent sequences: A394072 A394073 A394074 * A394076 A394077 A394078

Keyword

nonn,cons,easy

Author

Paolo Xausa, Mar 19 2026

Status

approved