Base | Number of Dots |

Triangle | \[\frac{1}{6}n(n+1)(n+2)\] |

Square | \[\frac{1}{6}n(n+1)(2n+1)\] |

Pentagon | \[\frac{1}{2}n^2(n+1)\] |

Hexagon | \[\frac{1}{6}n(n+1)(4n-1)\] |

Heptagon | \[\frac{1}{6}n(n+1)(5n-2)\] |

Octagon | \[\frac{1}{2}n(n+1)(2n-1)\] |

n - gon | \[\frac{1}{6}n(n+1)(n(r-2)-(r-5))\] |

# Pyramidal Numbers

Triangular numbers are constructed starting with a single dot, then a triangle with a dot at each vertex, then a larger triangle with a dot between each two dots and so one. If these triangles are assembled into a pyramid, then the numbers of dots are called pyramidal numbers.