A394537 - OEIS

%I #11 May 22 2026 08:01:04

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

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

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

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

%H Paolo Xausa, <a href="/A394537/b394537.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>.

%F Equals sqrt(4 + csc(Pi/16)^2)/4.

%F Equals the largest root of 512*x^8 - 1536*x^6 + 1280*x^4 - 416*x^2 + 47.

%e 1.3755485807735077126939276792065837776863256143470...

%t First[RealDigits[Sqrt[4 + Csc[Pi/16]^2]/4, 10, 100]] (* or *)

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

%Y Cf. A394534 (volume), A394535 (surface area), A394536 (midradius), A394538 (height).

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

%K nonn,cons,easy

%O 1,2

%A _Paolo Xausa_, Apr 08 2026