A378351 - OEIS

%I #5 Nov 28 2024 11:10:54

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

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

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

%N Decimal expansion of the surface area of a (small) triakis octahedron with unit shorter edge length.

%C The (small) triakis octahedron is the dual polyhedron of the truncated cube.

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

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

%F Equals 3*sqrt(7 + 4*sqrt(2)) = 3*sqrt(7 + A010487).

%e 10.672941873983546705150008922490160564590104237715...

%t First[RealDigits[3*Sqrt[7 + Sqrt[32]], 10, 100]] (* or *)

%t First[RealDigits[PolyhedronData["TriakisOctahedron", "SurfaceArea"], 10, 100]]

%Y Cf. A378352 (volume), A378353 (inradius), A201488 (midradius), A378354 (dihedral angle).

%Y Cf. A377298 (surface area of a truncated cube with unit edge).

%Y Cf. A010487.

%K nonn,cons,easy,new

%O 2,3

%A _Paolo Xausa_, Nov 23 2024