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The compound of 5 octahedra is the dual of this compound of 5 cubes.
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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.
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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.
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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.
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The five octahedron compound contained with an icosidodecahedron.
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The nets printed onto metallic paper.
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One of the nets cut out. I also made an extra piece to fit inside the
base of each part for added strength.
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Two finished spikes. You can see how the extra part fits in here.
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Two spikes attached.
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Continue adding spikes.
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Just five spikes to go.
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