Figurate number

Derivation of hyperpyramidal figurate numbers from a left-justified Pascal's triangle.
  Natural numbers
  Triangular numbers
  Tetrahedral numbers
  Pentatope numbers
  5-simplex numbers
  6-simplex numbers
  7-simplex numbers

The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes (polygonal numbers) and different dimensions (polyhedral numbers). The term can mean

  • polygonal number
  • a number represented as a discrete r-dimensional regular geometric pattern of r-dimensional balls such as a polygonal number (for r = 2) or a polyhedral number (for r = 3).
  • a member of the subset of the sets above containing only triangular numbers, pyramidal numbers, and their analogs in other dimensions.[1]
  1. ^ Dickson, L. E. (1919). History of the Theory of Numbers. Vol. 2. p. 3. ISBN 978-0-8284-0086-2. Retrieved 2021-08-15.