In the centre
In geometry, a centre (or center) (from Greek κέντρον) of an object is a point in some sense in the middle of the object. According to the specific definition of center taken into consideration, an object might have no center. If geometry is regarded as the study of isometry groups then a centre is a fixed point of all the isometries which move the object onto itself. For objects with several symmetries, the centre of symmetry is the point left unchanged by the symmetric actions. So the centre of a square, rectangle, rhombus or parallelogram is where the diagonals intersect, this being (amongst other properties) the fixed point of rotational symmetries. Similarly the centre of an ellipse or a hyperbola is where the axes intersect.
Needless to say I like this composition