The word corner is actually not a defined term in mathematics. Many people refer to the vertex as a corner and many say corner and mean the vertex and the sides near it.
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A polygon has as many corners (vertices) as it has sides.
A triangle is the only polygon with 3 corners (vertices). There is no polyhedron with 3 corners.
A pentagon is any polygon with 5 sides and 5 corners.
Hexagon A polygon with 6 corners is a hexagon, the prefix hex means six.
4 sides and 4 corners because it is a quadrilateral polygon