A379708 - OEIS

%I #16 May 24 2026 00:37:27

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

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

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

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

%C The disdyakis triacontahedron is the dual polyhedron of the truncated icosidodecahedron (great rhombicosidodecahedron).

%H Paolo Xausa, <a href="/A379708/b379708.txt">Table of n, a(n) for n = 2..10000</a>

%H Polytope Wiki, <a href="https://polytope.miraheze.org/wiki/Disdyakis_triacontahedron">Disdyakis triacontahedron</a>.

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

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

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

%F Equals sqrt(22626/5 + 9738/sqrt(5)) = sqrt(22626/5 + 9738/A002163).

%F Minimal polynomial: 25*x^4 - 226260*x^2 + 37792656. - _Amiram Eldar_, May 24 2026

%e 94.234632662193735601503506520549159874997310453708...

%t First[RealDigits[Sqrt[22626/5 + 9738/Sqrt[5]], 10, 100]]

%t (* Alternative: *)

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

%o (PARI) sqrt(22626/5 + 9738/sqrt(5)) \\ _Charles R Greathouse IV_, Oct 10 2025

%Y Cf. A379709 (volume), A379710 (inradius), A379388 (midradius), A379711 (dihedral angle).

%Y Cf. A377796 (surface area of a truncated icosidodecahedron (great rhombicosidodecahedron) with unit edge length).

%Y Cf. A002163.

%K nonn,cons,easy

%O 2,1

%A _Paolo Xausa_, Dec 31 2024