Nested Polyhedra
Posted by
Joined Sep 18, '17 

I’m Robin, it’s a pleasure to meet you.


I’ve been circling this idea for a while, wanting to nest one polyhedron inside another, but I could never decide on a method to calculate the angles and sizes. Short version: I figured it out.


  • 1/8 BB plywood.
  • It’s a bear to put together. Gotta take your time, the model gets very rigid as it gets more complete.
  • 5 different parts, a total of 240 pieces.
  • Overall size: 5" diameter
  • No glue.

The three quarters view is probably the best for seeing the inner and outer structures. Inside is a icosahedron, outside is a dodecahedron. (for some reason it won't upload again, so scroll back up.)

You get some fun symmetries when you start aligning the model in certain ways,


It can look radically different depending in the viewing angle.


Overall, the design is really sturdy, despite the fact that the struts are only 0.125" x 0.125" thick. I may scale the connectors up and see about making this at a very large scale. As it stands now the longest elements are the dodecahedron edges, at 1.44". I could jump that up to be 19" long, I wonder how large the model would be? Let’s go see. HAH! It’d be 71" in diameter, just under six feet. That’s crazy. Like “can’t fit into the house” crazy. I wonder if the 1/8" baltic would stand up at that size or if it would collapse under its own weight?


Anyway, there you go, the latest creature.

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