Icosahedral and Octahedral shades

thingiverse

Triangular faces can be combined to form regular tetrahedra (four triangles, three faces per vertex), octahedra (eight triangles, four faces per vertex), and icosahedra (twenty triangles, five faces per vertex). This is an attempt at triangular face sections to build regular polyhedra for decorative purposes. The primary design goal is to allow simple assembly without the need for fasteners or other materials. All pieces slide together, and hold with friction and tension. Secondary considerations are overall aesthetics, hints at other geometries, and scalability and extensibility to various materials. Faces are laser-cut from sheets of mid-to-heavy card stock. Each sheet contains ten trigonal faces. Print two sheets to yield twenty faces. Assembled icosahedron is approximately 5.5 inches in diameter. Ensure that the slots (six per face) are cut all the way through by the laser; if not, use a knife to clean up the cuts. To assemble, start with two faces. Line up the slots on both edges, then gently slide together. If the slots won't line up at all, flip the new piece over: all slots on all faces must be oriented the same way. Take a third face and attach it to the second piece. Slide one edge onto the second face. If the edges are not properly aligned, gently wiggle/pull/push the material until the slots line up. The fourth piece is attached to the third piece, continuing to form a ring or bowl. The fifth piece is initially attached to the fourth, completing the ring/bowl around a single vertex. It is then attached to the first piece, forming a shallow bowl. Note that each vertex (i.e. the corner where all faces meet) has exactly five faces: each vertex in an icosahedron is the intersection of exactly five faces. It may be necessary to carefully bend the outer tabs a little in order to get the slots to line up. Just do it slowly and carefully to avoid tearing or permanently bending the material. Repeat assembly by adding one face at a time, building up a vertex to five faces. The last two faces can be a little tricky to slide into place. Just work slowly to carefully position the face roughly in place, with the tabs appropriately over/under, and gently line up all the slots. Octahedral assembly involves joining four faces around a single vertex, then attaching the fourth to the first. Add a fifth face to an edge of the bowl. Add a sixth face to the fifth, then attach one of its edges to the bowl. Add the seventh and eighth in the same manner as the sixth.