There are various characteristics and attributes that would describe a sphere. A sphere is a perfectly symmetrically round or circular three dimensional object.
A sphere has one point of symmetry (at its very center) if one considers rotational symmetry in its three dimensions. If one is only considering reflectional symmetry, it would have an infinite number of lines of symmetry.
a sphere or 3D circle
By saying: It is a red sphere.
A sphere would fit the given description
A circle or a sphere would seem to fit the given conditions
No, the center of mass of a body is a point where the entire mass of the body can be considered to be concentrated. If there is no mass at a point, the center of mass cannot exist at that point.
Technically you can not trace a sphere. If the base conditions are the same as for the other solid shapes, for example a cylinder, there is a base on which the cylinder rests, which creates the circle when it is traced. A sphere on a base would be touching in one point, which would be a dot. If you trace half a sphere, yes, than you do get a circle.
the gradient of a graph at any point.
It's the middle point of line. Hardly! How far would that be from a point 3/4 way along the line? Try centre of a circle, or of a sphere.
The focal point is in front of the retina
Since a "face" is usually defined as a flat area and no area of a sphere is flat, the answer would be NO. It is possible to place two planes tangent to the surface of the sphere and parallel to each other, but each plane will only touch the surface of the sphere at a single point rather than coinciding with a "face".