# Icosahedral Number

Given a number n, find the n-th icosahedral number. The **Icosahedral Number** is class of figurative number that represents an icosahedron(a polyhedron with 20 faces) Source : Wiki).

The first few Icosahedral Numbers are 1, 12, 48, 124, 255, 456, 742, 1128, 1629…………..

** Examples :**

Input : 5 Output :255 Input :10 Output :2260

**n-th ** term of Icosahedral Number is given by:

Basic implementation of the above idea:

## C++

`// Icosahedral number to find ` `// n-th term in C++ ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function to find ` `// Icosahedral number ` `int` `icosahedralnum(` `int` `n) ` `{ ` ` ` `// Formula to calculate nth ` ` ` `// Icosahedral number & ` ` ` `// return it into main function. ` ` ` `return` `(n * (5 * n * n - 5 * n + 2)) / 2; ` `} ` ` ` `// Driver Code ` `int` `main() ` `{ ` ` ` `int` `n = 7; ` ` ` ` ` `cout << icosahedralnum(n); ` ` ` `return` `0; ` `} ` |

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## Java

`// Icosahedral number to find ` `// n-th term in Java ` `import` `java.io.*; ` ` ` `class` `GFG { ` ` ` ` ` `// Function to find ` ` ` `// Icosahedral number ` ` ` `static` `int` `icosahedralnum(` `int` `n) ` ` ` `{ ` ` ` `// Formula to calculate nth ` ` ` `// Icosahedral number & ` ` ` `// return it into main function. ` ` ` ` ` `return` `(n * (` `5` `* n * n - ` `5` `* ` ` ` `n + ` `2` `)) / ` `2` `; ` ` ` `} ` ` ` ` ` `// Driver Code ` ` ` `public` `static` `void` `main (String[] args) ` ` ` `{ ` ` ` `int` `n = ` `7` `; ` ` ` `System.out.println( ` ` ` `icosahedralnum(n)); ` ` ` `} ` `} ` ` ` `// This code is contributed by aj_36. ` |

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## Python3

`# Python 3 Program to find ` `# nth Icosahedral number ` ` ` `# Icosahedral number ` `# number function ` `def` `icosahedralnum(n) : ` ` ` ` ` `# Formula to calculate nth ` ` ` `# Icosahedral number ` ` ` `# return it into main function. ` ` ` `return` `(n ` `*` `(` `5` `*` `n ` `*` `n ` `-` ` ` `5` `*` `n ` `+` `2` `)) ` `/` `/` `2` ` ` ` ` `# Driver Code ` `if` `__name__ ` `=` `=` `'__main__'` `: ` ` ` ` ` `n ` `=` `7` ` ` `print` `(icosahedralnum(n)) ` ` ` `# This code is contributed aj_36 ` |

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## C#

`// Icosahedral number to ` `// find n-th term in C# ` `using` `System; ` ` ` `class` `GFG ` `{ ` ` ` ` ` `// Function to find ` ` ` `// Icosahedral number ` ` ` `static` `int` `icosahedralnum(` `int` `n) ` ` ` `{ ` ` ` `// Formula to calculate ` ` ` `// nth Icosahedral number ` ` ` `// & return it into main ` ` ` `// function. ` ` ` `return` `(n * (5 * n * n - ` ` ` `5 * n + 2)) / 2; ` ` ` `} ` ` ` ` ` `// Driver Code ` ` ` `static` `public` `void` `Main () ` ` ` `{ ` ` ` `int` `n = 7; ` ` ` `Console.WriteLine(icosahedralnum(n)); ` ` ` `} ` `} ` ` ` `// This code is contributed by ajit ` |

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## PHP

`<?php ` `// Icosahedral number to ` `// find n-th term in PHP ` ` ` `// Function to find ` `// Icosahedral number ` `function` `icosahedralnum(` `$n` `) ` `{ ` ` ` `// Formula to calculate nth ` ` ` `// Icosahedral number & ` ` ` `// return it into main function. ` ` ` `return` `(` `$n` `* (5 * ` `$n` `* ` `$n` `- ` ` ` `5 * ` `$n` `+ 2)) / 2; ` `} ` ` ` `// Driver Code ` `$n` `= 7; ` ` ` `echo` `icosahedralnum(` `$n` `); ` ` ` `// This code is contributed by m_kit ` `?> ` |

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**Output**

742

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