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Small Snub Icosicosidodecahedron

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  • Vertex description: 5/2.3.3.3.3.3
  • Faces: 112
  • Edges: 180
  • Vertices: 60
  • External facelets: 212
  • Dual: Small Hexagonal Hexecontahedron

This is the simplest of the nonconvex snub uniform polyhedra. All the faces are regular, but intersecting. Each vertex is surrounded by six faces: five triangles and one pentagram. The 60 white triangles are the snub faces, meaning they share no symmetry with the overall polyhedron. There are also 40 blue triangles which overlap in pairs forming 6-pointed stars. These faces share 3-fold rotational symmetry with the parent polyhedron. And finally there are 12 green pentagrams.

This polyhedron demonstrates that snub polyhedra may still have mirror-symmetry overall. The "snub" part referring to the fact that some faces do not share any symmetry with the polyhedron.

Each different type of net for the model, as printed by Great Stella. The dark piece at the back is an extra piece used to add internal support.
Let's get started! Here are the first parts glued together.
From beneath, with the additional part for added internal support glued into place.
About half way now.
And from underneath.
Looks finished from this side...
...but isn't finished yet. From below we see more of the extra parts glued in place for added strength.
Starting to close up now.
To put the last piece in, I created the cap, seen here behind to the left. This will fit over the almost-complete model.
Once the last five 6-pointed stars are in place, we need to cut them down a bit so that the cap will fit over them easily. The cap can then sit on top, and each 6-pointed star can be glued down one at a time.

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