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Model Gallery Cube-octahedron compound

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Stellated icosahedron

Cube-octahedron compound
18 Feb 2006
Test model of cube-octahedron compound, in cardstock

I started putting together a "shape library" with a list of supported (and unsupported) solids, with links to MathWorld. This particular shape can be viewed here.

Basically, take a cube, merge it with an octahedron (the test model I made says "tetrahedron" on the octahedron faces - but that's a misnomer) and you have what is shown here.

Papercut doesn't currently support this as a primitive shape, but it's easy enough to create. You'll need version 2.0.286 or later to create this shape. Just create an octahedron and k-stellate it with a custom factor of 70.71% and voila! you have the cube-octahedron compound. This is the same technique (albeit with a different k-stellate factor) used to create Kepler's Stella Octangula.

OK, why 70.71%??? This is the inverse of the square root of 2, and is the relationship between the cube edge lengths and octahedron edge lengths in this compound figure. Check here for the math...


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