A394071 - OEIS

%I #18 Jul 20 2026 23:42:03

%S 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,

%T 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,

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

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

%H Paolo Xausa, <a href="/A394071/b394071.txt">Table of n, a(n) for n = 1..10000</a>

%H David I. McCooey, <a href="https://dmccooey.com/polyhedra/HeptagonalAntiprism.html">Heptagonal Antiprism</a>.

%H Polytope Wiki, <a href="https://polytope.miraheze.org/wiki/Heptagonal_antiprism">Heptagonal 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 (7/24)*(cot(Pi/7) + cot(Pi/14))*sqrt(4 - sec(Pi/14)^2) = (7/24)*(A178818 + cot(A019681))*sqrt(4 - sec(A019681)^2).

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

%e 3.233915292855978877348368198023350486655463938323...

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

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

%o (PARI) 7/24*(cos(Pi/7)/sin(Pi/7)+cos(Pi/14)/sin(Pi/14))*sqrt(4-1/cos(Pi/14)^2) \\ _Charles R Greathouse IV_, Jul 20 2026

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

%Y Cf. A394076, A394077 (dihedral angles).

%Y Cf. A019681, A178818.

%K nonn,cons,easy,changed

%O 1,1

%A _Paolo Xausa_, Mar 10 2026