A071402 Rounded volume of a regular icosahedron with edge length n.

0, 2, 17, 59, 140, 273, 471, 748, 1117, 1590, 2182, 2904, 3770, 4793, 5987, 7363, 8936, 10719, 12724, 14964, 17454, 20205, 23231, 26545, 30160, 34089, 38345, 42942, 47893, 53209, 58906, 64995, 71490, 78404, 85749, 93540, 101789, 110509

Offset: 0

Author

Rick L. Shepherd, May 29 2002

Keywords

• easy
• nonn

Comments

The printed reference given shows in a table on p. 10 that Volume is "2.18170a^3" (a is edge). Both PARI (see Example here) and a handheld calculator show that 2.18169 is correct for a 5-decimal-place approximation.

Examples

			a(6)=471 because round(6^3*(3 + sqrt(5))*5/12) = round(216*2.181694990...) = round(471.24...) = 471.
		

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

Crossrefs

Cf. A000578 (cube), A071399 (tetrahedron), A071400 (octahedron), A071401 (dodecahedron), A071398 (total surface area of icosahedron).

Cf. A102208 ((3+Sqrt(5)) * 5/12).

Programs

Magma

[Round(n^3 * (3+Sqrt(5)) * 5/12): n in [0..50]]; // Vincenzo Librandi, May 21 2011

PARI

for(n=0,100,print1(round(n^3*(3+sqrt(5))*5/12),","))

Formula

a(n) = round(n^3 * (3+sqrt(5)) * 5/12).