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Compound of 5 Octahedra

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A compound of 5 octahedra. This model is provided in Small Stella, Great Stella and Stella4D's Polyhedron Libraries. It is a stellation of the icosahedron, and a faceting of the icosidodecahedron.

The compound of 5 octahedra is the dual of this compound of 5 cubes.
The stellation diagram of the icosahedron, with the appropriate cells selected to generate the compound of 5 octahedra. You can create the compound yourself using Great Stella or Stella4D's stellation tools.
Here we see how a single octahedron fits around an icosahedron. The compound consists of all fice octahedra that can be fitted around a single icosahedron in this way.
Here's the facet required to generate the compound as a faceting of the icosidodecahedron. Again, you can create this easily with Stella's faceting tools. Remember to enable "Options→Maintain Reflexibility" as rotating the facet over the symmetry group would otherwise only generate half the faces. You need reflected copies of the facet too.
The five octahedron compound contained with an icosidodecahedron.
The nets printed onto metallic paper.
One of the nets cut out. I also made an extra piece to fit inside the base of each part for added strength.
Two finished spikes. You can see how the extra part fits in here.
Two spikes attached.
Continue adding spikes.
Just five spikes to go.

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