Well, honey, shapes that have only flat surfaces are called polygons. Think of your squares, triangles, and pentagons - they're all as flat as a pancake. So, if you're looking for some dimensionless divas, polygons are where it's at.
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Shapes have flat surfaces in plane geometry. They can also be described as two dimensional shapes.
cube There are a great many solid shapes that have only flat surfaces.
cube
It has three shapes. Two surfaces are flat circles and one is a curved rectangle.
A cylinder
Polygons are flat shapes