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I agree with Kreesanya. A triangle is a geometric shape, and it cannot be physically "touched." One can only touch a model of this geometric shape.
The concept of a triangle itself is a kind of mathematical abstract noun, while "the external form of an object" is a specific noun used to name an object that is externally similar in shape. One cannot touch an abstract object.
A simple example: it is impossible to touch such abstract concepts as "a person's intelligence" or "love." These may not be the best examples, but the essence is the same.