# Dodecahedral number

Given a number n, the task is to find **n-th ** dodecahedral number.

A dodecahedral number belongs to a figurate number and represents it dodecahedron.

First few Dodecahedral number (where n = 0, 1, 2, 3…….) are : 0, 1, 20, 84 and so on.

**Examples :**

Input : 2 Output : 20 Input :8 Output :2024

Mathematics formula for ** nth** dodecahedral number:

## C++

`// C++ program to find nth ` `// dodecahedral number ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function to find ` `// dodecahedral number ` `int` `dodecahedral_num(` `int` `n) ` `{ ` ` ` `// Formula to calculate nth ` ` ` `// dodecahedral number ` ` ` `// and return it into main function. ` ` ` `return` `n * (3 * n - 1) * (3 * n - 2) / 2; ` `} ` ` ` `// Driver Code ` `int` `main() ` `{ ` ` ` `int` `n = 5; ` ` ` `// print result ` ` ` `cout << n << ` `"th Dodecahedral number: "` `; ` ` ` `cout << dodecahedral_num(n); ` ` ` `return` `0; ` `} ` |

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## Java

`// Java program to find nth dodecahedral ` `// number ` `import` `java.io.*; ` ` ` `class` `GFG { ` ` ` ` ` `// Function to find dodecahedral number ` ` ` `static` `int` `dodecahedral_num(` `int` `n) ` ` ` `{ ` ` ` ` ` `// Formula to calculate nth ` ` ` `// dodecahedral number ` ` ` `// and return it into main function. ` ` ` `return` `n * (` `3` `* n - ` `1` `) * ` ` ` `(` `3` `* n - ` `2` `) / ` `2` `; ` ` ` `} ` ` ` ` ` `// Driver Code ` ` ` `public` `static` `void` `main (String[] args) ` ` ` `{ ` ` ` `int` `n = ` `5` `; ` ` ` `// print result ` ` ` `System.out.print( n + ` `"the Dodecahedral"` ` ` `+ ` `" number:"` `); ` ` ` `System.out.println( dodecahedral_num(n)); ` ` ` `} ` `} ` ` ` `// This code is contributed by anuj_67. ` |

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## Python3

`# Python program to find ` `# nth dodecahedral number ` ` ` `# Function to calculate ` `# dodecahedral number ` ` ` `def` `dodecahedral_num(n): ` ` ` ` ` `# Formula to calculate nth ` ` ` `# dodecahedral number ` ` ` ` ` `return` `n ` `*` `(` `3` `*` `n ` `-` `1` `) ` `*` `(` `3` `*` `n ` `-` `2` `) ` `/` `/` `2` ` ` `# Driver Code ` `n ` `=` `5` `print` `(` `"%sth Dodecahedral number :"` `%` `n, ` ` ` `dodecahedral_num(n)) ` ` ` `# This code is contributed by ajit. ` |

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## C#

`// C# program to find nth dodecahedral ` `// number ` `using` `System; ` ` ` `class` `GFG { ` ` ` ` ` `// Function to find dodecahedral number ` ` ` `static` `int` `dodecahedral_num(` `int` `n) ` ` ` `{ ` ` ` ` ` `// Formula to calculate nth ` ` ` `// dodecahedral number ` ` ` `// and return it into main function. ` ` ` `return` `n * (3 * n - 1) * ` ` ` `(3 * n - 2) / 2; ` ` ` `} ` ` ` ` ` `// Driver Code ` ` ` `public` `static` `void` `Main () ` ` ` `{ ` ` ` `int` `n = 5; ` ` ` ` ` `// print result ` ` ` `Console.Write( n + ` `"the Dodecahedral"` ` ` `+ ` `" number:"` `); ` ` ` `Console.WriteLine( dodecahedral_num(n)); ` ` ` `} ` `} ` ` ` `// This code is contributed by anuj_67. ` |

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## PHP

`<?php ` `// PHP program to find nth ` `// dodecahedral number ` ` ` ` ` `// Function to find ` `// dodecahedral number ` `function` `dodecahedral_num( ` `$n` `) ` `{ ` ` ` `// Formula to calculate nth ` ` ` `// dodecahedral number ` ` ` `// and return it into main function. ` ` ` `return` `$n` `* (3 * ` `$n` `- 1) * ` ` ` `(3 * ` `$n` `- 2) / 2; ` `} ` ` ` `// Drivers Code ` `$n` `= 5; ` ` ` `// print result ` `echo` `$n` `, ` `"th Dodecahedral number: "` `; ` `echo` `dodecahedral_num(` `$n` `); ` ` ` `// This code is contributed by vt_m ` `?> ` |

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**Output :**

5th Dodecahedral number: 455

Reference: https://en.wikipedia.org/wiki/Dodecahedral_number

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