Any shape with straight edges can have perpendicular edges.
A triangular pyramid has 6 edges.
Oval
A circle or a sphere perhaps?
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.
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.
hexagon
An Octagon
A pentagon
hexagon
Polyhedra.
octagon !
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.