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

3,4

Links

Table of n, a(n) for n=3..92.

Eric Weisstein's World of Mathematics, Truncated Dodecahedron.

Wikipedia, Truncated dodecahedron.

Formula

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

Example

100.990760153101988544745948988636656554915090575...

Mathematica

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

Crossrefs

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

Cf. A131595 (analogous for a regular dodecahedron).

Cf. A002194, A010476.

Sequence in context: A199960 A257176 A324859 * A090655 A334480 A229758

Adjacent sequences: A377691 A377692 A377693 * A377695 A377696 A377697

Keyword

nonn,cons,easy

Author

Paolo Xausa, Nov 04 2024

Status

approved