A071398 Rounded total surface area of a regular icosahedron with edge length n.

0, 9, 35, 78, 139, 217, 312, 424, 554, 701, 866, 1048, 1247, 1464, 1697, 1949, 2217, 2503, 2806, 3126, 3464, 3819, 4192, 4581, 4988, 5413, 5854, 6313, 6790, 7283, 7794, 8323, 8868, 9431, 10011, 10609, 11224, 11856, 12505, 13172, 13856, 14558, 15277

Offset: 0

Author

Rick L. Shepherd, May 29 2002

Keywords

• easy
• nonn

Examples

			a(4)=139 because round(5*4^2*sqrt(3)) = round(80*1.73205...) = round(138.56...) = 139.
		

References

• S. Selby, editor, CRC Basic Mathematical Tables, CRC Press, 1970, pp. 10-11.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Icosahedron
• Eric Weisstein's World of Mathematics, Platonic Solid

Crossrefs

Cf. A070169 (tetrahedron), A033581 (cube), A071396 (octahedron), A071397 (dodecahedron), A071402 (volume of icosahedron).

Programs

Magma

[Round(5 * n^2 * Sqrt(3)): n in [0..50]]; // Vincenzo Librandi, May 21 2011

Mathematica

With[{c=5Sqrt[3]},Round[c Range[0,50]^2]] (* Harvey P. Dale, May 20 2011 *)

PARI

for(n=0,100,print1(round(5*n^2*sqrt(3)),","))

Python

from math import isqrt
def A071398(n): return (m:=isqrt(k:=75*n**4))+int(k>m*(m+1)) # Chai Wah Wu, Jun 05 2025

Formula

a(n) = round(5 * n^2 * sqrt(3)).