A364896 - OEIS

%I #13 Jun 12 2024 17:07:06

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

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

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

%N Decimal expansion of the 4-volume of the unit regular 120-cell.

%C Decimal expansion of (1575+705*sqrt(5))/4.

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

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/120-cell">120-cell</a>

%e Equals 787.85698103433793399211...

%t First[RealDigits[(1575 + 705*Sqrt[5])/4, 10, 100]] (* _Paolo Xausa_, Jun 12 2024 *)

%o (PARI) (1575+705*sqrt(5))/4

%Y Decimal expansion of 4-volumes: A364895 (5-cell), A000007 = 1 (8-cell or tesseract), A020793 = 1/6 (16-cell), A000038 = 2 (24-cell), this sequence (120-cell), A364897 (600-cell).

%Y Cf. A102769 (decimal expansion of the volume of the unit regular dodecahedron).

%K nonn,cons

%O 3,1

%A _Jianing Song_, Aug 12 2023