A379709 Decimal expansion of the volume of a disdyakis triacontahedron with unit shorter edge length.

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

Offset

2,1

Comments

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

Links

Paolo Xausa, Table of n, a(n) for n = 2..10000

Polytope Wiki, Disdyakis triacontahedron.

Eric Weisstein's World of Mathematics, Disdyakis Triacontahedron.

Wikipedia, Disdyakis triacontahedron.

Index entries for algebraic numbers, degree 4.

Formula

Equals sqrt(88590 + 39612*sqrt(5))/5 = sqrt(88590 + 39612*A002163)/5.

Minimal polynomial: 125*x^4 - 885900*x^2 + 527076. - Amiram Eldar, May 24 2026

Example

84.1819754400481313518959942929339817444032991207...

Mathematica

First[RealDigits[Sqrt[88590 + 39612*Sqrt[5]]/5, 10, 100]]
(* Alternative: *)
First[RealDigits[PolyhedronData["DisdyakisTriacontahedron", "Volume"], 10, 100]]

Prog

(PARI) sqrt(88590 + 39612*sqrt(5))/5 \\ Charles R Greathouse IV, Oct 10 2025

Crossrefs

Cf. A379708 (surface area), A379710 (inradius), A379388 (midradius), A379711 (dihedral angle).

Cf. A377797 (volume of a truncated icosidodecahedron (great rhombicosidodecahedron) with unit edge length).

Cf. A002163.

Sequence in context: A021547 A154527 A145435 * A197477 A381395 A133839

Adjacent sequences: A379706 A379707 A379708 * A379710 A379711 A379712

Keyword

nonn,cons,easy

Author

Paolo Xausa, Dec 31 2024

Status

approved