It is the only polygon whose side lengths determine its shape.
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A triangle is a 3 sided polygon
What is the special name for the segment that connects the center of a regular polygon to an outer edge to form the height of a triangle
A triangle is a polygon, though trigon is an alternative name for a 3 sided polygon.
A triangle is a polygon with 3 sides
There is no special name. In a prism it would be a quadrilateral, in an antiprism, a triangle.