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Every shape that is round does not have edges. A shape that has sharp points and has straight lines can have edges.
a stupid shape
any polygon
There is no such shape. A 2d shape with 5 sides and all equal angles must be a regular pentagon (or a 5-pointed star if you stretch the definition of "all angles"). And a regular pentagon - or star - has 5 lines of symmetry.
A symmetrical shape is a mirror image of a shape when a line is drawn through it and some shapes have many lines of symmetry or none at all.