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Many dictionaries define tetrahedron and tetrahedral in connection with the geometrical shape. Can I use tetrahedral as an adjective for a phenomenon that has four aspects? e.g.

The tetrahedral inductive framework of emotional intelligence

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    If you are speaking to mathematicians, chemists or physicists, you could probably get away with it. For the lay-person, you would probably not be understood. Four-pronged would be much more understood.
    – Adam
    Commented Aug 31, 2015 at 20:30
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    Or four-cornered.
    – mkennedy
    Commented Aug 31, 2015 at 21:09
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    Don't give up on getting a better answer than my comment. I don't think four-pronged is perfect for you either. To me, "n-pronged" works better to describes processes, rather than structures. "Tetrahedral" is probably the perfect word, except that even most college graduates probably don't know what it means.... Maybe four-faceted?
    – Adam
    Commented Aug 31, 2015 at 21:09
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    Or four-sided... Commented Aug 31, 2015 at 21:12
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    Pyramidal would be evocative, although it might require a tiny bit of explanation, especially if the four points are all meant to have equal import.
    – Adam
    Commented Aug 31, 2015 at 21:14

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I would generally argue against it. I would probably use four-fold to describe something with four equally-ranked aspects. Quadruple is another option. Four-pronged, from the comments, can also be useful; I would consider it if the four aspects are separate in some sense, but tending in the same direction.

There is an exception: if the analogy to a tetrahedron is especially evocative of the relationship between the four aspects that you are describing. A tetrahedron can be defined either by its sides or its vertices. So, if it is really useful to think of the four aspects as equidistant points or as planes that share a single edge with each of the other planes, then maybe the term would be useful.

I don't find any dictionary definitions of tetrahedral that include the kind of usage you want. However, that alone should not be enough to dissuade you; English is flexible enough to accommodate metaphorical uses such as this one. However, it does mean that using the word in this manner is uncommon, and so would impose what you might call a "readability cost" on your audience. If you are not getting a benefit in communication substantial enough to outweigh that cost (such as I described in the last paragraph), then you're better off making another choice.

Although "tetrahedron" is not very uncommon, and many people would be familiar with "tetra-" as meaning four, a tetrahedron is composed of triangular faces, which could muddy your meaning. Another source of confusion is the similar use of dimensions as analogous to aspects: square for two, cube for three. Describing something as "cubic" metaphorically conjures a sense of three, not six.

I think a usage like this should convey a really important point in a really useful way to make up for either your reader pausing to figure out what you mean, or for you having to explain yourself.

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