Here's a couple examples of the same technique applied in a slightly different variation, to output entirely different results.  Using just a few different versions of the polyhedron, and leaving the internal faces intact, we could create an almost endless array of object conditions.  These might be useful for a nice hanging lampshade, for example:

In Blender, you might want to start by using the Ico Sphere primitive, or the Platonic, Archemedian, or Catalan Solids Addon, found under the Add Mesh > Math Function > Solids menu.

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