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Great Dirhombicosidodecahedron ("Miller's Monster")

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  • Vertex description: (5/
  • Faces: 124 (24 pentagrams, 40 triangles, 60 squares)
  • Edges: 240
  • Vertices: 60
  • External facelets: 1280
  • Dual: Great Dirhombicosidodecacron

This model has 1280 external facelets to put together! The polyhedron is uniform, so all the faces are regular although it's hard to make them all out. It is the only uniform polyhedron with as many as 8 faces meeting at each vertex (two purple pentagrams, two red triangles, and four yellow squares). It is also the only uniform polyhedron with snub faces other than triangles. Here they are squares. All faces occur in coplanar pairs, with the squares passing through the centre of the polyhedron.

This model has an edge length of about 21.6 centimetres, and a diameter of 30.6 centimetres. The nets filled up 42 A4 pages! 10 red, 9 purple and 23 yellow.

Here is one of each different net printed by Great Stella.
Start like this, then add the red triangle pairs all around.
This is then surrounded by five of the part shown here. Above is the finished piece, below is the same piece at an earlier stage.
Should end up like this. You'll need 12 of this part. The parts from the previous step can also be glued to each other using tabs that have already been glued once. Note: such tabs are available from both sides. One should be glued behind, the other left unglued in front. This will be bent forward and glued to yet another part later. After this I added the purple triangle pairs all around (pentagram arms), but realised later it was easier to continue another way. The purple triangle pairs are most easily added after all the other parts are connected.
Here is the above part flipped over (it also has the purple triangle pairs added). A bit of extra support is used inside (the green parts, not seen from outside the model). These were created and printed out using Stella's faceting mode.
Here are a few parts connected together. At this stage I was still adding those purple triangle pairs all around.
These are the small parts that hold the bigger parts above together. You'll need 20 of these.
Eventually I hit upon a better way to proceed. Leave the purple triangle pairs till the end and use the part from the previous step to connect everything together. This part is glued to the free tab mentioned eariler.
Proceeding this way makes the last part a lot easier (and the earlier parts for that matter). Here we are ready for the last section to be slotted in.
The last section has now been slotted in and glued in place with those free tabs. All that's left is to glue the purple triangle pairs in place.

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