A395164 Decimal expansion of the volume of a uniform 9-gonal antiprism with unit edges.

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

Offset

1,1

Links

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

Polytope Wiki, Enneagonal antiprism.

Eric Weisstein's World of Mathematics, Antiprism.

Wikipedia, Antiprism.

Index entries for algebraic numbers, degree 6.

Formula

Equals (3/8)*sqrt(1 + 2*cos(Pi/9))*csc(Pi/9)^2 = (3/8)*sqrt(1 + A332437)*A121602^2.

Equals the largest real root of 64*x^6 - 1872*x^4 - 648*x^2 + 81.

Example

5.439735529893062827340996528202566456746765891602...

Mathematica

First[RealDigits[3*Sqrt[1 + 2*Cos[Pi/9]]*Csc[Pi/9]^2/8, 10, 100]]
(* Alternative: *)
First[RealDigits[PolyhedronData["NonagonalAntiprism", "Volume"], 10, 100]]

Crossrefs

Cf. A395165 (surface area), A395166 (midradius), A395167 (circumradius), A395168 (height).

Cf. A395169, A395170 (dihedral angles).

Cf. A121602, A332437.

Sequence in context: A202412 A194556 A154198 * A086793 A070515 A096733

Adjacent sequences: A395161 A395162 A395163 * A395165 A395166 A395167

Keyword

nonn,cons,easy

Author

Paolo Xausa, Apr 21 2026

Status

approved