Wythoff construction

Wythoff construction is a method in geometry for creating uniform polyhedra and tilings by systematically placing vertices relative to a symmetrical framework. Starting with a regular polygon or polyhedron, points are added along symmetry lines or points that divide angles in specific ratios. Connecting these points according to certain rules produces a new, more complex shape with uniform properties—meaning identical vertices and regular faces. This process leverages symmetry and geometric ratios to generate diverse, highly symmetric structures, often used in mathematical art, crystallography, and modeling advanced geometric forms.