Shape Computation Lab

Find Polygons in a 5-Star Polygon

Tzu-Chieh Kurt Hong


This video showcases how an initial model of a regular 5-star polygon can be queried and restructured in a series of different closed polygons under similarity transformations. The video starts with the query of an isosceles triangle whose pair of angles are coincident with the angles of the regular 5-star pentagon to show five matches under similarity transformations. The next examples show the searches for two types of quadrilaterals, one convex and one concave, that both yield five matches each; a regular pentagon that yields one match; and a concave heptagon that yields five matches again, all under similarity transformations. In all cases, the Shape Machine calculates the exact number of matches without any duplicates.