A378973 Decimal expansion of the surface area of a triakis icosahedron with unit shorter edge length.

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

Offset: 2

Author

Paolo Xausa, Dec 13 2024

Keywords

• nonn
• cons
• easy

Comments

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

Examples

			26.228595976743751681458195104356801731865266699519...
		

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. A378974 (volume), A378975 (inradius), A378976 (midradius), A378977 (dihedral angle).

Cf. A377694 (surface area of a truncated dodecahedron with unit edge length).

Cf. A002163.

Programs

Mathematica

First[RealDigits[3*Sqrt[(173 - 9*Sqrt[5])/2], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["TriakisIcosahedron", "SurfaceArea"], 10, 100]]

Formula

Equals 3*sqrt((173 - 9*sqrt(5))/2) = 3*sqrt((173 - 9*A002163)/2).