I was just reading about polyhedrons and wondered, even though it's an impossible shape, what a 3-hedron is called? I'm really asking what the Greek for '3'. Does it just converge to a triangle?
What do you call a 3-hedron?
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$\begingroup$
geometry
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0["tri"](http://www.merriam-webster.com/dictionary/tri) seems like the right prefix, coming from Latin and Greek. – 2012-01-08
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0That was my first thought, though thought 'tri' was only Latin. – 2012-01-08
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2A relevant reference: http://en.wikipedia.org/wiki/Number_prefix – 2012-01-08
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0how about three-hedron? lol – 2012-01-08
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0I call him Harvey – 2012-01-08
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0Do you mean a [tetrahedron](http://en.wikipedia.org/wiki/Tetrahedron)? – 2012-01-08
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2@J.D.: No, tetrahedrons have 4 faces, not 3. The question is at face value asking about an object that doesn't exist, but is really asking about a prefix meaning $3$. – 2012-01-08
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0@JonasMeyer, it does exist, for appropriate values of «exist». An orthant deserves to be called a trihedron! – 2012-01-08
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0In the right ambient space, a trihedron makes sense and can exist. It's just as in spherical geometry (on the two-sphere), where you can start a figure with an angle at the north pole by drawing two longitude lines southward that will meet again at the south pole at the same angle. So in $S^3$, you can draw a trihedral angle at one pole, and continue the three “planes” to the opposite pole, where they will meet again. – 2012-01-08
1 Answers
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Tri- is the greek prefix.
We do use the word trihedron, but to refer to something slightly different: the Frenet-Serret trihedron.