A379386 Decimal expansion of the volume of a deltoidal hexecontahedron with unit shorter edge length.

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

Offset

2,1

Comments

The deltoidal hexecontahedron is the dual polyhedron of the (small) rhombicosidodecahedron.

Links

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

Polytope Wiki, Deltoidal hexecontahedron.

Eric Weisstein's World of Mathematics, Deltoidal Hexecontahedron.

Wikipedia, Deltoidal hexecontahedron.

Index entries for algebraic numbers, degree 4.

Formula

Equals sqrt((29530 + 13204*sqrt(5))/9) = sqrt((29530 + 13204*A002163)/9).

Minimal polynomial: 81*x^4 - 531540*x^2 + 292820. - Amiram Eldar, Jun 09 2026

Example

81.004143635377089099456665341616282246804393456803...

Mathematica

First[RealDigits[Sqrt[(29530 + 13204*Sqrt[5])/9], 10, 100]]
(* Alternative: *)
First[RealDigits[PolyhedronData["DeltoidalHexecontahedron", "Volume"], 10, 100]]

Crossrefs

Cf. A379385 (surface area), A379387 (inradius), A379388 (midradius), A379389 (dihedral angle).

Cf. A185093 (volume of a (small) rhombicosidodecahedron with unit edge length).

Cf. A002163.

Sequence in context: A375078 A365237 A342980 * A094922 A230049 A088990

Adjacent sequences: A379383 A379384 A379385 * A379387 A379388 A379389

Keyword

nonn,cons,easy,changed

Author

Paolo Xausa, Dec 23 2024

Status

approved