A397543 - OEIS

%I #12 Jul 02 2026 08:07:24

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

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

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

%N Decimal expansion of the surface area of a canonical (dual-uniform) pentagonal trapezohedron with unit short edge length.

%C The pentagonal trapezohedron is the dual polyhedron of the pentagonal antiprism.

%H Paolo Xausa, <a href="/A397543/b397543.txt">Table of n, a(n) for n = 2..10000</a>

%H David I. McCooey, <a href="https://dmccooey.com/polyhedra/PentagonalTrapezohedron.html">Pentagonal Trapezohedron</a>.

%H Polytope Wiki, <a href="https://polytope.miraheze.org/wiki/Pentagonal_antitegum">Pentagonal antitegum</a>.

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

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

%H <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>.

%F Equals 5*(1 + s)^2*sqrt((1 - s)/2 + s + 2)/4, where s = sqrt(5) = A002163.

%F Equals the largest root of x^4 - 625*x^2 + 3125.

%e 24.898982848827802734015846213978370554090497058946...

%t First[RealDigits[Root[#^4 - 625*#^2 + 3125 &, 4], 10, 100]]

%t (* Alternative: *)

%t First[RealDigits[PolyhedronData[{"Trapezohedron", 5}, "SurfaceArea"], 10, 100]]

%Y Cf. A384871 (volume), A237603 (inradius), A239798 (midradius), A397544 (height).

%Y Cf. A104457 (long edge).

%Y Cf. A019692 (small face angle * 10), A228719 (large face angle), A137218 (dihedral angle).

%Y Cf. A384625 (surface area of the dual + 10).

%Y Cf. A002163.

%K nonn,cons,easy

%O 2,1

%A _Paolo Xausa_, Jun 30 2026