A378712 - OEIS

%I #9 Dec 08 2024 02:43:52

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

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

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

%N Decimal expansion of the surface area of a disdyakis dodecahedron with unit shorter edge length.

%C The disdyakis dodecahedron is the dual polyhedron of the truncated cuboctahedron (great rhombicuboctahedron).

%H Paolo Xausa, <a href="/A378712/b378712.txt">Table of n, a(n) for n = 2..10000</a>

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

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Disdyakis_dodecahedron">Disdyakis dodecahedron</a>.

%F Equals (6/7)*sqrt(783 + 436*sqrt(2)) = (6/7)*sqrt(783 + 436*A002193).

%e 32.066734010531944413349823874895723462863495851553...

%t First[RealDigits[6/7*Sqrt[783 + 436*Sqrt[2]], 10, 100]] (* or *)

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

%Y Cf. A378713 (volume), A378714 (inradius), A378393 (midradius), A378715 (dihedral angle).

%Y Cf. A377343 (surface area of a truncated cuboctahedron (great rhombicuboctahedron) with unit edge length).

%Y Cf. A002193.

%K nonn,cons,easy

%O 2,1

%A _Paolo Xausa_, Dec 06 2024