A379132 - OEIS

%I #12 Feb 05 2025 10:22:58

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

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

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

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

%C The pentakis dodecahedron is the dual polyhedron of the truncated icosahedron.

%H Paolo Xausa, <a href="/A379132/b379132.txt">Table of n, a(n) for n = 2..10000</a>

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

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

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

%F Equals (5/3)*sqrt((421 + 63*sqrt(5))/2) = (5/3)*sqrt((421 + 63*A002163)/2).

%e 27.93524960070079310581019127996368070525778610907...

%t First[RealDigits[5/3*Sqrt[(421 + 63*Sqrt[5])/2], 10, 100]] (* or *)

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

%o (PARI) sqrt((421 + 63*sqrt(5))/2)*5/3 \\ _Charles R Greathouse IV_, Feb 05 2025

%Y Cf. A379133 (volume), A379134 (inradius), A379135 (midradius), A379136 (dihedral angle).

%Y Cf. A377750 (surface area of a truncated icosahedron with unit edge length).

%Y Cf. A002163.

%K nonn,cons,easy,changed

%O 2,1

%A _Paolo Xausa_, Dec 16 2024