Pascal's triangle Construct a "d"-dimensional triangle (a 3-dimensional triangle is a tetrahedron) by placing additional dots below an initial dot, corresponding to P(1) = 1. Place these dots in a manner analogous to the placement of numbers in Pascal's triangle. To find P("x"), have a total of "x" dots composing the target shape. P("x") then equals the total number of dots in the shape. A 0-dimensional triangle is a point and a 1-dimensional triangle is simply a line, and therefore P("x") = "1" and P("x") = "x", which is the sequence of natural numbers. The number of dots in each layer corresponds
Schläfli symbol Schläfli symbol In geometry, the Schläfli symbol is a notation of the form {p,q,r...} that defines regular polytopes and tessellations. The Schläfli symbol is named after the 19th-century Swiss mathematician Ludwig Schläfli, who made important contributions in geometry and other areas. The Schläfli symbol is a recursive description, starting with "{p}" for a "p"-sided regular polygon that is convex. For example, {3} is an equilateral triangle, {4} is a square, {5} a convex regular pentagon and so on. Regular star polygons are not convex, and their Schläfli symbols {"p"/"q"} contain irreducible fractions "p"/"q", where "p" is the number of vertices.