Construction automation system and method

A method for forming at least a portion of a polyhedron, said method comprising:

• (a) determining a pattern for each of a plurality of courses constituting the polyhedron based on the type of the polyhedron and the frequency of the polyhedron;
• (b) determining a unique group of triangular-shaped objects from each of said plurality of courses, wherein a plurality of said unique group of triangular-shaped objects constitute each of said plurality of courses and each said unique group of triangular-shaped objects comprises a specific number of two types of triangular-shaped objects, a specific order of said two types of triangular-shaped objects and a specific orientation of said two types of triangular-shaped objects, said two types of triangular-shaped objects comprise a first type of objects, wherein five of said first type of objects constitute a pentagon and a second type of objects, wherein six of said second type of objects constitute a hexagon;
• (c) determining members of said unique group of triangular-shaped objects and an orientation of each said member of said unique group of triangular-shaped objects;
• (d) determining an order in which said members of said unique group of triangular-shaped objects are laid within a course of said plurality of courses;
• and
• (e) laying said members of said unique group of triangular-shaped objects as determined from steps (a)-(d) to form the at least a portion of the polyhedron.