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

Author

Paolo Xausa, Dec 23 2024

Keywords

• nonn
• cons
• easy

Comments

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

Examples

			2.634797688222471365013793337475980265570278715884...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Deltoidal Hexecontahedron.
• Wikipedia, Deltoidal hexecontahedron.

Crossrefs

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

Cf. A002163.

Programs

Mathematica

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

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.