Constructing an Octahedron Inside a Circle WITHOUT a Compass.

In this video, I’m constructing an octahedron inside a circle using simple geometric arcs. I start with a clean circle, drawn lightly on scratch paper. Instead of a traditional compass, I’m using my Mathomat circle arc template, which lets me step off equal arcs smoothly and consistently around the circumference. By marking six evenly spaced points on the circle, the geometry begins to emerge. Connecting these points forms our perspective, and from there the hidden structure of the octahedron becomes visible. The intersecting arcs define the remaining vertices above and below the center. What I like about this method is how physical and intuitive it feels. With just a circle, repeated distances, and careful line work, a three-dimensional solid appears from a flat surface.This is classical construction—simple tools, precise relationships, and elegant results.