A378974 Decimal expansion of the volume of a triakis icosahedron with unit shorter edge length.

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

Offset: 2

Author

Paolo Xausa, Dec 14 2024

Keywords

• nonn
• cons
• easy

Comments

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

Examples

			12.017220926874316513329814423376647765182009668737...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 2..10000
• Eric Weisstein's World of Mathematics, Triakis Icosahedron.
• Wikipedia, Triakis icosahedron.

Crossrefs

Cf. A378973 (surface area), A378975 (inradius), A378976 (midradius), A378977 (dihedral angle).

Cf. A377695 (volume of a truncated dodecahedron with unit edge length).

Cf. A002163.

Programs

Mathematica

First[RealDigits[(19 + 13*Sqrt[5])/4, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["TriakisIcosahedron", "Volume"], 10, 100]]

Formula

Equals (19 + 13*sqrt(5))/4 = (19 + 13*A002163)/4.