strictly platonic

ya

This is something I made, as a gift for someone, out of beads. Maybe the colors don't seem that exciting, but the person's favorite color is brown, so. . . . I made this video to help me visualize this shape should I decide to make another in the future, so that I can create color schemes that exploit the structure. Special thanks are due to SaboCatGirl, whose camera was used to create the video, and who edited the music into the background. The figure is a polyhedron known as a stellated dodecahedron. It was made by creating 30 diamond shaped pieces from beads and wire, and sewing them together, with wire, in the appropriate fashion. The idea was to make something which was three dimensional, but had a lot of symmetry. As far as polyhedra (3D polygons) with maximal symmetry go, the range of choices is fairly limited: one has tetrahedra, cubes, octohedra, dodecahedra, and icosohedra (the Platonic solids). It is a little problematic to make something like a pentagon from beads tho, whereas adding the stellation allows you to just use simple diamond shapes. Basically, instead of having a plain dodecahedron, you instead are looking at a dodecahedron with a spike jutting out of each face.

This is a stellated cube, basically a cube with a spike out of each face. This was part of a Christmas present for SaboCatGirl, who kindly filmed the video at my request. The video stars SaboCatGirl as the craft handler. This one is much easier to visualize than something like the stellated dodecahedron, but there are some effects that I wanted to have captured on video to remind myself of later. The first is the fact that the faces can be collected into four triangles. This is reminiscent of the tetrahedron, but since the cube is dual to the octohedron (see my comments on the dodecahedron video) I'm not sure how the triangles arise. I could just be a coincidence. The other aspect is the color scheme, which I have by now realized stems from the coordinate system in three dimensions--the color of a given diamond is determined by which coordinate axis it is aligned with.

Just thought I would upload this, for the sake of completeness, so that I will have a video posted of stellations of all the Platonic solids. . . only a video of the stellated tetrahedron remains. That one is less taxing to make than the others, so maybe it won't be too long before I get around to it. . .

This is the stellated icosohedron. Rather hard to visualize, so I kept track of how it should be put together by exploiting the duality between the icosohedron and dodecahedron. While this one probably looks the most impressive, it takes about the same amount of work as a dodecahedron. This completes my making the full zoo of stellated platonic solids, although I never made videos of two of them.