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Compound of 5 Cubes

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This compound of 5 cubes was first described by Edmund Hess in 1876 and has been a favourite amongst geometers ever since. It may be created as a faceting of the dodecahedron, or a stellation of the rhombic triacontahedron, and has icosahedral symmetry overall. This model was made from nets printed using Stella, and is available in Small Stella, Great Stella and Stella4D.

The compound of 5 cubes is the dual of this compound of 5 octahedra.
Here's how a single cube fits within a dodecahedron. Its vertices align with 8 of the dodecahedron's vertices. A cube can fit like this into a single dodecahedron in 5 different ways. Put all 5 together to get the compound of 5 cubes.
The five cube compound contained with a dodecahedron. You could create the compound yourself using Great Stella or Stella4D's faceting mode.
The stellation diagram of the rhombic triacontahedron, with appropriate cells selected to generate the compound of 5 cubes. You could create the compound yourself using Great Stella or Stella4D's stellation tools.
Print the nets from Stella. Stella can group parts of the same colour together, which I did here in order to print directly onto the coloured metallic paper that I used. Parts fitted onto one sheet of each colour. Start by putting pieces together like this.
Then attach to form stars like this. Be careful to get the colouring right after the first one! You may want to ask Stella to print edge connection IDs to help you attach parts correctly.
The same part upside down.
For added strength, and keeping in mind how I will get the last piece in, I printed some extra parts for added internal strength. Here is one such part, which attaches to the part above.
I also added a second extra part to add strength to the central part of the star. It's the white part in the centre of this picture.
Construct 12 parts as above, being careful of colouring, and the attach the 12 parts like faces of a dodecahedron. Here are the first two parts connected.
Same as above, viewed from the other side.
Half of the model complete.
Getting there.
Just one part left to attach. The above construction makes it easier to put the last part in, though you have to put glue on ten tabs at once here before easing the last part into place. Came together quite well in the end.

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