A378975 Decimal expansion of the inradius of a triakis icosahedron with unit shorter edge length.

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

Offset: 1

Author

Paolo Xausa, Dec 14 2024

Keywords

• nonn
• cons
• easy

Comments

The triakis icosahedron is the dual polyhedron of the truncated dodecahedron.

Examples

			1.37451744701047164727510000639742367448102733307...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Triakis Icosahedron.
• Wikipedia, Triakis icosahedron.

Crossrefs

Cf. A378973 (surface area), A378974 (volume), A378976 (midradius), A378977 (dihedral angle).

Cf. A002163.

Programs

Mathematica

First[RealDigits[Sqrt[(477 + 199*Sqrt[5])/488], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["TriakisIcosahedron", "Inradius"], 10, 100]]

Formula

Equals sqrt((477 + 199*sqrt(5))/488) = sqrt((477 + 199*A002163)/488).