The term "trigon" is another word for triangle. Related terms are trilateral and deltoid.
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if it does have corners its not a triangle
Depending on how you use it, another word for it could be vertex, like in an isosceles triangle, or peak, if used in a pyramid.
Equilateral triangle, regular triangle.
The expanded binomial is another name for Pascal's triangle.
Another name is its correct name: an isosceles triangle.