A379387 Decimal expansion of the inradius of a deltoidal hexecontahedron with unit shorter edge length.

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

Offset

1,1

Comments

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

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Deltoidal Hexecontahedron.

Wikipedia, Deltoidal hexecontahedron.

Formula

Equals 11*sqrt((135 + 59*sqrt(5))/205)/(7 - sqrt(5)) = 11*sqrt((135 + 59*A002163)/205)/(7 - A002163).

Equals the largest root of 820*x^4 - 5710*x^2 + 121.

Example

2.634797688222471365013793337475980265570278715884...

Mathematica

First[RealDigits[Root[820*#^4 - 5710*#^2 + 121 &, 4], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["DeltoidalHexecontahedron", "Inradius"], 10, 100]]

Crossrefs

Cf. A379385 (surface area), A379386 (volume), A379388 (midradius), A379389 (dihedral angle).

Cf. A002163.

Sequence in context: A261069 A236557 A359243 * A262943 A357735 A163892

Adjacent sequences: A379384 A379385 A379386 * A379388 A379389 A379390

Keyword

nonn,cons,easy

Author

Paolo Xausa, Dec 23 2024

Status

approved