Simplex Geometry
Simplex geometry is the study of the simplest possible shapes in any number of dimensions, like points, lines, triangles, and pyramids.
Think of it this way
A dot marks a single point on a cutting board. A line of peas in a row adds one dimension. Three peas flat on the board form a triangle, the simplest shape in two dimensions. Stack one pea on top and you get a pyramid, the simplest solid.
Explaining simplex geometry by grade level
A point is just a dot. Connect two dots and you get a line. Connect three dots and you get a triangle. These are the simplest shapes you can make, and each one uses one more dot than the last.