The infinigon is a graph constructed by inscribing a triangle into a circle, inscribing another circle inside the triangle, then inscribing a square inside the circle, followed by another circle, and so on, increasing the number of sides of each new polygon by one. A vertex is placed at each point of intersection. We rotate polygons clockwise when necessary to avoid overlapping vertices. In this paper, we will discuss properties of the infinigon, including vertex and edge counts, vertex degrees, Euler and Hamilton cycles, and chromatic numbers. We also give conjectures on properties related to distance.
展开▼
