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A stellate solid is one where each face of the solid has been replaced with a pyramid of the appropriate base shape. For example, a stellate cube would be a cube where each of the cube's six sides has been replaced with a square-based pyramid. Normally stellate objects are more complex and interesting than cubes. For example, you could make stellate dodecahedrons or icosahedrons.
I have seen geodesic domes that were stellate. Starting from a basic geodesic dome, the builders add short triangular pyramids. This HowTo shows how to generate the points for stellate geodesic spheres.
Start by building a geodesic sphere as described in the HowTo Make a geodesic sphere. Then replace each triangle in the sphere with a suitable pyramid. Figure 1 shows the results. The image on the left shows the results as a wireframe with hidden surfaces removed. The image on the right shows the result drawn using ray tracing.
Figure 1. A stellate geodesic sphere in wireframe and ray tracing.
Figure 2 shows the same stellate geodesic spheres but with taller pyramids.
Figure 2. A stellate geodesic sphere with taller pyramids.
Both of these images were drawn using the the VBRay program described in Chapter 17 of my book Visual Basic Graphics Programming. The wireframe images took 3 or 4 seconds while the ray traced versions took almost 28 minutes.
The example program available here for download generates face data that describes the stellate geodesic sphere for that program.
See also: Make a geodesic sphere.
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