This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A383955 #19 Aug 23 2025 14:44:39 %S A383955 1,1,6,9,8,3,9,4,2,0,4,6,1,9,2,5,9,2,2,6,7,5,8,0,9,6,2,2,1,4,2,8,1,1, %T A383955 6,1,1,3,6,1,2,7,8,0,4,3,9,7,1,5,9,2,8,5,3,0,7,7,6,7,4,3,8,2,5,8,2,9, %U A383955 0,1,3,5,5,2,5,3,5,2,2,4,3,3,1,6,2,0,8 %N A383955 Decimal expansion of sqrt(5/3 - 2*sqrt(1/45)). %C A383955 Let v_10 be a degree-10 vertex and v_3 be a degree-3 vertex of a triakis icosahedron centered at the origin. Then this is the ratio of norm(v_10)/norm(v_3). %C A383955 The minimal polynomial is 45*x^4 - 150*x^2 + 121. %C A383955 One choice of coordinates for the triakis icosahedron describes a degree-10 vertex of the triakis icosahedron as (0,1,(1+sqrt(5)/2)) and a degree-3 vertex as (5+7*sqrt(5)/22*(1, 1, 1). %H A383955 Wikipedia, <a href="https://en.wikipedia.org/wiki/Triakis_icosahedron#As_a_Catalan_solid">Triakis_icosahedron</a> %e A383955 1.169839420461925922675809622142811611361278... %t A383955 RealDigits[Sqrt[(25 - 2*Sqrt[5])/15], 10, 100][[1]] %Y A383955 Cf. A378973, A378974, A378975, A378976, A378977, A380793, A380794, A382009. %K A383955 nonn,cons,new %O A383955 1,3 %A A383955 _Peter Kagey_, Aug 19 2025