What is the term for all objects that share the following property
For any two different points in the shape the perpendicular bisector is an axis of symmetry of the shape.
So for 2 dimensional euclidean geometry it could be about a circle or a line
In 2 dimensional hyperbolic geometry it could be about a circle, line, horocycle or hypercycle
In 3 dimensionional euclidean geometry could be about a line circle, plane or a sphere. (The perpendicular bisector being a plane)
In 3 dimensions hyperbolic geometry could be about a line, circle, horocycle, hypercycle, plane, sphere, horosphere or hypersphere.
In other 3 dimensional geometries also other shapes could fall under this property.(am interested in which they are)
Bonus question: This property also seems to include other properties (the shape has a constant curvature being one of them, are there others?