A379708 Decimal expansion of the surface area of a disdyakis triacontahedron with unit shorter edge length.

9, 4, 2, 3, 4, 6, 3, 2, 6, 6, 2, 1, 9, 3, 7, 3, 5, 6, 0, 1, 5, 0, 3, 5, 0, 6, 5, 2, 0, 5, 4, 9, 1, 5, 9, 8, 7, 4, 9, 9, 7, 3, 1, 0, 4, 5, 3, 7, 0, 8, 1, 3, 1, 2, 1, 3, 8, 8, 6, 9, 4, 7, 9, 2, 6, 1, 9, 5, 9, 3, 1, 5, 5, 2, 8, 1, 8, 5, 8, 9, 0, 6, 7, 9, 3, 6, 7, 1, 2, 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(22626/5 + 9738/sqrt(5)) = sqrt(22626/5 + 9738/A002163).

Minimal polynomial: 25*x^4 - 226260*x^2 + 37792656. - Amiram Eldar, May 24 2026

Example

94.234632662193735601503506520549159874997310453708...

Mathematica

First[RealDigits[Sqrt[22626/5 + 9738/Sqrt[5]], 10, 100]]
(* Alternative: *)
First[RealDigits[PolyhedronData["DisdyakisTriacontahedron", "SurfaceArea"], 10, 100]]

Prog

(PARI) sqrt(22626/5 + 9738/sqrt(5)) \\ Charles R Greathouse IV, Oct 10 2025

Crossrefs

Cf. A379709 (volume), A379710 (inradius), A379388 (midradius), A379711 (dihedral angle).

Cf. A377796 (surface area of a truncated icosidodecahedron (great rhombicosidodecahedron) with unit edge length).

Cf. A002163.

Sequence in context: A319530 A388257 A395397 * A318410 A245298 A122952

Adjacent sequences: A379705 A379706 A379707 * A379709 A379710 A379711

Keyword

nonn,cons,easy

Author

Paolo Xausa, Dec 31 2024

Status

approved