A sphere
In three dimensions, the solid defined as being bound by the set of points at a given distance form a point is a sphere. In two dimensions, the figure defined as being bound by the set of points at a given distance from a point is a circle. In one dimension, a line segment is bound by the two points at a given distance from a point.
A circle is the set of all the points that are the same (arbitrary) distance (called the radius) from some (arbitrary) point (called the center).
It is a circle or a sphere
A circle or a sphere would fit the given description.
Sphere
They are called equidistant points and form points on a sphere for a solid or a circle on a plane figure.
if it's a circle, all points are equidistant from the center.
A sphere.
That's a figure called a "circle". The given distance is the circle's radius, and the point is its center.
A circle.
A sphere
a sphere
vertices
A circle or sphere.
A solid sphere perhaps?
A circle.