A377694 Decimal expansion of the surface area of a truncated dodecahedron with unit edge length.

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

Offset: 3

Author

Paolo Xausa, Nov 04 2024

Keywords

• nonn
• cons
• easy

Examples

			100.990760153101988544745948988636656554915090575...
		

Links

• Eric Weisstein's World of Mathematics, Truncated Dodecahedron.
• Wikipedia, Truncated dodecahedron.

Crossrefs

Cf. A377695 (volume), A377696 (circumradius), A377697 (midradius), A377698 (Dehn invariant, negated).

Cf. A131595 (analogous for a regular dodecahedron).

Cf. A002194, A010476.

Programs

Mathematica

First[RealDigits[5*(Sqrt[3] + 6*Sqrt[5 + Sqrt[20]]), 10, 100]] (* or *)
First[RealDigits[PolyhedronData["TruncatedDodecahedron", "SurfaceArea"], 10, 100]]

Formula

Equals 5*(sqrt(3) + 6*sqrt(5 + 2*sqrt(5))) = 5*(A002194 + 6*sqrt(5 + A010476)).