A394538 Decimal expansion of the height of a uniform octagonal antiprism with unit edges.

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

Offset

0,1

Links

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

David I. McCooey, Octagonal Antiprism.

Polytope Wiki, Octagonal antiprism.

Eric Weisstein's World of Mathematics, Antiprism.

Wikipedia, Antiprism.

Formula

Equals sqrt(1 - (sec(Pi/16)^2)/4) = sqrt((3 - A393638)/4).

Equals sqrt((1 + 2*cos(Pi/8))/(2 + 2*cos(Pi/8))) = sqrt((1 + A179260)/(2 + A179260)).

Equals the largest real root of 2*x^8 + 8*x^6 - 16*x^4 + 8*x^2 - 1.

Example

0.8602955698629715664423007760041056923313852176566964...

Mathematica

First[RealDigits[Sqrt[1 - (Sec[Pi/16]^2)/4], 10, 100]]

Prog

(PARI) polrootsreal(2*x^8 + 8*x^6 - 16*x^4 + 8*x^2 - 1)[6] \\ Charles R Greathouse IV, May 13 2026

Crossrefs

Cf. A394534 (volume), A394535 (surface area), A394536 (midradius), A394537 (circumradius).

Cf. A387320, A387323 (dihedral angles).

Cf. A179260, A393638.

Sequence in context: A100121 A010526 A199473 * A153617 A069855 A156551

Adjacent sequences: A394535 A394536 A394537 * A394539 A394540 A394541

Keyword

nonn,cons,easy

Author

Paolo Xausa, Apr 08 2026

Status

approved