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here are some paper constructions that are fun to make and I think theyre rather pretty there are seven different designs here that and try building each is made from one kind of regular polygon with slots on them for assembly the first one is made from 20 equilateral triangles of 5 different colors to understand the underlying mathematics start with a regular icosahedron it consists of 20 triangles 5 at each vertex then rotate each triangle 60 degrees so instead of meeting edge to edge they overlap through each other notice how just above the center of each triangle 3 vertices of the neighboring three triangles meet at a point and the edges outline lovely stars around each of the 12 openings so the triangle template has three slots going halfway across the line of intersection which is what allows the physical paper to pass through its neighboring triangles to assemble this we cut out 20 triangles with the slots you could do it all in one color but here I made four triangles in each