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A102769 Decimal expansion of the volume of a dodecahedron with each edge of unit length. 9


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

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

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

%N Decimal expansion of the volume of a dodecahedron with each edge of unit length.

%C Equals 5*phi^3/(2*xi^2), phi being the golden ratio (A001622) and xi its associate (A182007). - _Stanislav Sykora_, Nov 23 2013

%H Ivan Panchenko, <a href="/A102769/b102769.txt">Table of n, a(n) for n = 1..1000</a>

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

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Platonic_solid">Platonic solid</a>

%F Equals (15 + 7 sqrt(5)) / 4.

%F Equals (sqrt(5)/2)*(phi)^4, where phi is the golden ratio. - _G. C. Greubel_, Jul 06 2017

%e 7.663118960624631968716053920...

%p evalf((15+7*sqrt(5))/4,100); # _Wesley Ivan Hurt_, Jan 29 2017

%t RealDigits[(Sqrt[5]/2)*(GoldenRatio)^4, 10, 50][[1]] (* _G. C. Greubel_, Jul 06 2017 *)

%o (PARI) (7*sqrt(5)+15)/4 \\ _Charles R Greathouse IV_, Apr 25 2016

%Y Cf. A001622 (phi), A182007 (phi associate), A020829 (regular tetrahedron volume), A131594 (regular octahedron volume), A102208 (regular icosahedron volume).

%K nonn,cons

%O 1,1

%A Bryan Jacobs (bryanjj(AT)gmail.com), Feb 10 2005

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Last modified January 17 19:58 EST 2019. Contains 319251 sequences. (Running on oeis4.)