A394534 - OEIS

%I #14 Jul 26 2026 23:37:19

%S 4,2,6,7,9,5,6,7,5,0,4,5,7,1,3,6,6,7,0,7,9,0,4,3,6,3,5,0,6,5,3,3,4,1,

%T 9,3,1,2,4,6,9,8,5,7,3,7,3,2,9,1,1,3,1,2,9,5,7,9,7,2,8,5,4,6,7,7,7,5,

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

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

%H Paolo Xausa, <a href="/A394534/b394534.txt">Table of n, a(n) for n = 1..10000</a>

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

%H Polytope Wiki, <a href="https://polytope.miraheze.org/wiki/Octagonal_antiprism">Octagonal 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_08">Index entries for algebraic numbers, degree 8</a>.

%F Equals (2/3)*sqrt(2*(sqrt(2) + sqrt(103*sqrt(2) + 146) + 2)) = (2/3)*sqrt(2*(A002193 + sqrt(103*A002193 + 146) + 2)).

%F Equals the largest real root of 6561*x^8 - 46656*x^6 - 1410048*x^4 + 1511424*x^2 - 8192.

%e 4.2679567504571366707904363506533419312469857373291...

%t First[RealDigits[2*Sqrt[2*(2 + Sqrt[2] + Sqrt[146 + 103*Sqrt[2]])]/3, 10, 100]] (* or *)

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

%o (PARI) 2/3*sqrt(2*(sqrt(2)+sqrt(103*sqrt(2)+146)+2)) \\ _Charles R Greathouse IV_, Jul 26 2026

%Y Cf. A394535 (surface area), A394536 (midradius), A394537 (circumradius), A394538 (height).

%Y Cf. A387320, A387323 (dihedral angles).

%Y Cf. A002193.

%K nonn,cons,easy,changed

%O 1,1

%A _Paolo Xausa_, Apr 04 2026