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After building part of this model I decided it was too flexible for my
liking. I used "Selection>Mouse Selection Mode>Create
Facets" to create the small triangles shown here that fit across
each vertex.
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These can be glued to the existing tabs inside, and make the model a
lot more robust. Tip: you can set the net-spacing to zero when
you print out the triangles since they don't need tabs. This also
gives you the advantage that the negative regions between
triangles are also the same triangles, so there's less cutting
required.
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Close-up of model.
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Another close-up of model.
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These three models are related to each other. They all share the same
set of vertices and edges. Four faces surround a vertex in each model,
and you may think of these as being two pairs, chosen from a set of
three available pairs: (1) a pair of decagrams, (2) a triangle and a
pentagram, and (3) a pair of intersecting squares.
The great dodecicosidodecahedron has pairs (1) & (2).
The great rhombidodecahedron
has pairs (1) & (3).
The great rhombicosidodecahedron
has pairs (2) & (3).
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