a circle
A pedantic edit:
Also an ellipse or a wriggly loop.
Any shape that has no straight edges is described as a curvilinear shape.
Any shape with straight edges can have perpendicular edges.
A triangular pyramid has 6 edges.
A shape with no straight edges that can be described as looking like 'a squashed circle' is called an ellipse. This shape is also sometimes referred to as an oval.
Oval
A circle or a sphere perhaps?
Any shape with straight edges can have perpendicular edges.
Every shape that is round does not have edges. A shape that has sharp points and has straight lines can have edges.
Overall
An ellipse is a shape that could be described as looking like 'a squashed circle.' With no straight edges, this shape is also called an oval.
An Octagon
hexagon
A pentagon
hexagon
octagon !
Polyhedra.
A triangular pyramid has 6 edges.
The only regular geometric shape that fits your description would be an elipse. That is a circular shape so it has no straight edges, and appears to be a squashed circle.