Tiling on a Sphere
In this Assignment 0, we had to print an object based of our knowledge from the tutorials to illustrate symmetry or linear transformation. I chose to print an octagonal bipyramid in a heart of a sphere. In the following blog post, I will be explaining how I tried to illustrate both symmetry and linear transformation in my final 3D printed object.
An octagonal bipyramid (or dipyramid) is a polyhedron formed by joining two octagonal pyramids from their bases. That is in a way that the shared base of the two pyramids would be the primary symmetry plane that connects the pyramid to its mirror image. An octagonal pyramid has 16 triangle faces, 24 edges, and 10 vertices. All the faces of this bipyramid are isosceles triangles, meaning that it is face-transitive. Hence, all the faces lie within the same symmetry orbit.
The reason that I named this print “Tiling on a Sphere” because if you draw an imaginary sphere around this bipyramid, where all the vertices are tangible to the surface of the sphere, you will see a pattern of tiling on a sphere which represents the main domains of [4,2], 422 symmetry.
To help illustrate the tiling better, I designed the eight arcs to represents the planes of symmetry on imaginary sphere around the bipyramid.
I printed my object using the OpenSCAD and the Ultimaker. To hold the arcs aroung the bipyramid, I had to print using a little bit of support around the arcs and removed them later.
Octagonal Bipyramid: first, I started by printing 2 cones, using the cylinder command, and adjusted the number of fragments (fn) to 8, so that I would get an orthogonal pyramid with 8 equal sides for the base. Then using the rotate command, I transformed one of them 180 degrees over the x-y plane so that it would give me a bipyramid.
Tiling of the sphere: I started off by printing 4 identical rings using the difference command and then I adjusted the degree of rotation so that every ring would be connected to the vertices of the bi-pyramid.
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