A379710 Decimal expansion of the inradius of a disdyakis triacontahedron with unit shorter edge length.

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

Offset

1,1

Comments

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

Links

Paolo Xausa, Table of n, a(n) for n = 1..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(3477/964 + 7707/(964*sqrt(5))) = sqrt(3477/964 + 7707/(964*A002163)).

Minimal polynomial: 4820*x^4 - 34770*x^2 + 1089. - Amiram Eldar, Jun 09 2026

Example

2.679969340204835578579553327459806767085423038168...

Mathematica

First[RealDigits[Sqrt[3477/964 + 7707/(964*Sqrt[5])], 10, 100]]
(* Alternative: *)
First[RealDigits[PolyhedronData["DisdyakisTriacontahedron", "Inradius"], 10, 100]]

Crossrefs

Cf. A379708 (surface area), A379709 (volume), A379388 (midradius), A379711 (dihedral angle).

Cf. A002163.

Sequence in context: A102046 A397945 A019913 * A299421 A327181 A047554

Adjacent sequences: A379707 A379708 A379709 * A379711 A379712 A379713

Keyword

nonn,cons,easy

Author

Paolo Xausa, Dec 31 2024

Status

approved