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I'm looking for single words to describe interior (as in 'corner of a room') and exterior angles (as in 'corner of a building').

For the exterior angle I found quoin which is (according to Merriam-Webster) 'a solid exterior angle (as of a building)' and '(architecture) solid exterior angle of a building; especially one formed by a cornerstone' according to the Free Dictionary, so it's spot on.

Now, how could I describe an interior angle? If there's no single word for this, perhaps a phrase sounding better than 'concave corner' or 'interior angle corner'?

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Why did you need this word, if I may ask? –  Andres Riofrio Apr 8 '12 at 1:59
    
@AndresRiofrio I was preparing designs for a lamp which could be put on a flat wall, a quoin or in a dihedral and wanted to differentiate the three attachment types concisely and unambiguously. –  Gilead May 11 at 13:55
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up vote 3 down vote accepted

I don't know if it's an antonym for quoin, but in mathematics and rock climbing, there is the term dihedral.

mathematical dihedral

rock climbing diheral

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I agree with this answer, and have up-voted it. –  Hexagon Tiling Apr 7 '12 at 9:32
    
'Dihedral' it is, then :) Sounds very mathematical indeed but it is a single word so yay! :) JLG, @Hexagon Tiling. –  Gilead Apr 7 '12 at 12:08
    
@Gilead: ...except that 'dihedral' only describes the meeting of two planes, not the 'inside' (or 'outside') of the angle formed. –  Mitch Apr 7 '12 at 12:10
    
@Mitch: I thought of that before deciding to agree with it. I looked up the term "dihedral" in a mathematics dictionary (Penguin's), and it did not specify which of the two angles was meant, however, it is the convention that for two rays emanating from a common point, the "angle between them" is the smaller of the two angles, so I just scaled this up to the 3D case and went with the presumed convention that the smaller of the two angles was intended (which therefore means the interior angle, assuming, plausibly, that we're dealing with a convex structure). –  Hexagon Tiling Apr 7 '12 at 12:39
    
@Mitch: From what I read elsewhere (and what is in JLG's picture above) it means an intersection of two infinite planes in which case all corners (angles) are <=180 degrees, i.e. what we get is a flat surface or four interior angles. So yes, I would have preferred a clearly architectural and unambiguous term like 'quoin' but I think this should do. –  Gilead Apr 7 '12 at 13:12
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