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What is the appropriate usage of "symmetrical" and "symmetric" (using the geometrical adjectival definition of both terms)? Are they synonymous?

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At least in a mathematical context, I think "symmetric" is far more common. For one thing, there are many technical terms where "symmetric" is the correct choice (e.g. "symmetric space", "symmetric relation", "symmetric group"). I can't think of any technical term including "symmetrical". – Sam Lisi Apr 27 '12 at 7:54
Thanks for that last link @RegDwightΒВBẞ8, the answers there are great. – naught101 Apr 27 '12 at 13:31
up vote 2 down vote accepted

Merriam-Webster lists symmetric as being a variant of symmetrical, which is the 'official' dictionary entry:

symmetrical, adj : 1 : having or involving symmetry : exhibiting symmetry : exhibiting correspondence in size and shape of parts : BALANCED, REGULAR {the human body is symmetrical} {crystals are often symmetrical} {a symmetrical garden} {a symmetrical grouping}

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"Symmetrical" is a non-technical term, to describe any object that has symmetry; for example, a human face. "Symmetric" means "relating to symmetry", and is also used in a number of technical mathematical contexts (see Sam Lisi's comment under the question).

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So is en.wiktionary.org/wiki/symmetric wrong? – naught101 Apr 27 '12 at 8:56
@naught101: how do you think the wiktionary definitions are inconsistent with David's? – Mitch Apr 27 '12 at 14:44
I don't agree with symmetrical being a nontechnical term. Dorland's Medical Dictionary lists only "symmetrical," and the definition is: "pertaining to or exhibiting symmetry; in chemistry, denoting compounds which contain atoms or groups at equal intervals in the molecule." (Sounds technical to me.) – JLG Apr 27 '12 at 14:54
@mitch, because symmetric is defined as "symmetrical" - I assume that's supposed to mean it's a perfect synonym. – naught101 Apr 27 '12 at 15:12
@naught101: 1) there are no perfect synonyms. Ever. And a crowd sourced definition ain't gonna specify enough to judge. 2) wiktionary is not definitive. Don't take anything it says as gospel or draw logical conclusions from it. Frankly the same could be said for the OED, but wiktionary is not written by people who have spent a long time judging such things. – Mitch Apr 27 '12 at 16:23

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