A395164 - OEIS

%I #18 May 22 2026 07:56:05

%S 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,

%T 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,

%U 2,5,6,6,7,2,6,1,4,2,0,6,9,2,0,0,9,4,0,9,5,4

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

%H Paolo Xausa, <a href="/A395164/b395164.txt">Table of n, a(n) for n = 1..10000</a>

%H Polytope Wiki, <a href="https://polytope.miraheze.org/wiki/Enneagonal_antiprism">Enneagonal antiprism</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Antiprism.html">Antiprism</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Antiprism">Antiprism</a>.

%H <a href="/index/Al#algebraic_06">Index entries for algebraic numbers, degree 6</a>.

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

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

%e 5.439735529893062827340996528202566456746765891602...

%t First[RealDigits[3*Sqrt[1 + 2*Cos[Pi/9]]*Csc[Pi/9]^2/8, 10, 100]]

%t (* Alternative: *)

%t First[RealDigits[PolyhedronData["NonagonalAntiprism", "Volume"], 10, 100]]

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

%Y Cf. A395169, A395170 (dihedral angles).

%Y Cf. A121602, A332437.

%K nonn,cons,easy

%O 1,1

%A _Paolo Xausa_, Apr 21 2026