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DaveC426913

Gold Member

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I've got a 3D shape that, um, inherits from a cube (i.e. it retains properties characteristic of cubes). It has high symmetry.

I wish to string all its vertices (of which there are 16) with - I dunno, yarn - forming the edges (of which there are 32). I can do the entire thing with a single piece of yarn (all vertices have an even number of edges, thus no loose ends); AND I can join the loose ends together, making a single

(For comparison, this

Now all I want to do is ensure that my

Is there a science to this?

Alternately, I could turn this into a teaser and leave you guys to figure it out...

I'll give you a giant hint: its Schläfli symbol is {4,4} (square faces, 4 faces per vertex).

I wish to string all its vertices (of which there are 16) with - I dunno, yarn - forming the edges (of which there are 32). I can do the entire thing with a single piece of yarn (all vertices have an even number of edges, thus no loose ends); AND I can join the loose ends together, making a single

*loop*of yarn. I have physically proven this to be true.(For comparison, this

*cannot*be done with a regular cube, since all vertices have an odd number of edges, meaning all vertices will need an end of the yarn.)Now all I want to do is ensure that my

*pattern*of stringing is as symmetrical as possible, i.e. even accounting for the stringing pattern, there should still be at least some symmetry. ISTM, rotational symmetry is the strictest.Is there a science to this?

Alternately, I could turn this into a teaser and leave you guys to figure it out...

I'll give you a giant hint: its Schläfli symbol is {4,4} (square faces, 4 faces per vertex).

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