A140457 Decimal expansion of surface area of unit elongated dodecahedron.

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

Offset

2,2

References

H. S. M. Coxeter, Regular Polytopes, 3rd ed. New York: Dover, 1973.

E. S. Fedorov, "Elemente der Gestaltenlehre", Mineralogicheskoe obshchestvo Leningrad, Verhandlungen der Russisch-Kaiserlichen Mineralogischen Gesellschaft zu St. Petersburg 21, 1885, 1-279.

A. E. H. Tutton, Crystallography and Practical Crystal Measurement, London, 1922, pp. 567 (Fig. 448) and 723 (Fig. 585).

Links

Table of n, a(n) for n=2..124.

Polytope Wiki, Elongated rhombic dodecahedron.

Eric W. Weisstein, Elongated Dodecahedron.

Wikipedia, Elongated_dodecahedron.

Index entries for algebraic numbers, degree 4.

Formula

Equals 2*sqrt(3)*(3 + sqrt(5)) = A010469*(1+A098317).

Minimal polynomial: x^4 - 336*x^2 + 2304. - Amiram Eldar, Jun 09 2026

Example

18.138271537828097532....

Mathematica

RealDigits[2*Sqrt[3]*(3+Sqrt[5]), 10, 130][[1]] (* Harvey P. Dale, Nov 26 2011 *)

Crossrefs

Cf. A339528.

Sequence in context: A127454 A093602 A011469 * A358286 A176457 A110194

Adjacent sequences: A140454 A140455 A140456 * A140458 A140459 A140460

Keyword

cons,easy,nonn

Author

Jonathan Vos Post, Jun 26 2008

Extensions

Offset corrected and more digits added by R. J. Mathar, Jan 26 2009

Status

approved