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A378713 Decimal expansion of the volume of a disdyakis dodecahedron with unit shorter edge length.

%I A378713 #12 Feb 05 2025 10:40:59
%S A378713 1,6,2,8,8,9,1,9,0,8,2,9,2,3,5,2,5,0,3,8,5,0,3,1,2,2,5,0,3,6,1,9,4,4,
%T A378713 1,0,4,5,9,9,6,7,9,7,4,4,7,3,5,7,0,2,7,2,1,7,2,4,8,7,2,2,8,3,5,7,8,3,
%U A378713 7,0,1,3,4,1,5,1,8,7,0,4,9,5,9,7,6,5,0,6,9,2
%N A378713 Decimal expansion of the volume of a disdyakis dodecahedron with unit shorter edge length.
%C A378713 The disdyakis dodecahedron is the dual polyhedron of the truncated cuboctahedron (great rhombicuboctahedron).
%H A378713 Paolo Xausa, <a href="/A378713/b378713.txt">Table of n, a(n) for n = 2..10000</a>
%H A378713 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DisdyakisDodecahedron.html">Disdyakis Dodecahedron</a>.
%H A378713 Wikipedia, <a href="https://en.wikipedia.org/wiki/Disdyakis_dodecahedron">Disdyakis dodecahedron</a>.
%H A378713 <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>.
%F A378713 Equals sqrt(3*(2194 + 1513*sqrt(2)))/7 = sqrt(6582 + 4539*A002193)/7.
%e A378713 16.288919082923525038503122503619441045996797447357...
%t A378713 First[RealDigits[Sqrt[6582 + 4539*Sqrt[2]]/7, 10, 100]] (* or *)
%t A378713 First[RealDigits[PolyhedronData["DisdyakisDodecahedron", "Volume"], 10, 100]]
%o A378713 (PARI) sqrt(3*(2194 + 1513*sqrt(2)))/7 \\ _Charles R Greathouse IV_, Feb 05 2025
%Y A378713 Cf. A378712 (surface area), A378714 (inradius), A378393 (midradius), A378715 (dihedral angle).
%Y A378713 Cf. A377344 (volume of a truncated cuboctahedron (great rhombicuboctahedron) with unit edge length).
%Y A378713 Cf. A002193.
%K A378713 nonn,cons,easy
%O A378713 2,2
%A A378713 _Paolo Xausa_, Dec 07 2024