Metagons

Metagons: Atomic Star Graphs on Polygons

Metagons are polygons that feature atomic star graphs, and their decompositions embedded on the surfaces of polygons. The examples below—ranging from triangular to hexagonal—demonstrate both geometric metagons (where elements do not overlap) and center-to-midpoint versions. While center-to-vertex versions are also possible, they are not depicted here.

Atomic graphs are the simplest type of graph, consisting of a single node with two or more open links. When embedded onto regular polygons, these atomic graphs can be combined to create Kepler graphs, Kepler diagrams, and intricate designs that help identify and classify geometric and topological structures.

These concepts were developed concurrently and independently by both me and mathematical artist Robert Fathauer. Their versatility allows them to be explored through various mediums:

Print & Play DIY – Print metagon templates and experiment with paper constructions.

Woodcraft & CNC – Create precision-cut wooden metagons tiles.

3D Printing – Design and print abutting metagon tiles for hands-on exploration.

Digital & Interactive – Imagine an app where metagons become a virtual manipulative for geometric play and discovery.

Metagons bridge mathematical structure and artistic creativity, offering new ways to visualize and interact with Kepler Graphs and geometry.