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I am trying to model this thing, but the silver cover on top is what I have no idea how to go about.

And the blue-ish reflection I believe is from the sphere being cast on the inner side of the silver bits.

Any help would be much appreciated.

enter image description here

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Just create your sphere and over it draw the shape of your cuts using a Bezier Curve object.

Adjust its shape as necessary, then use knife project to cut the shape.

Bezier Curve

In object mode select your curve, then without deselecting, select your sphere, by this specific order. Enter edit mode on the sphere and with all faces selected use Knife Project with the option Cut Through active.

enter image description here

Carefully select all the unwanted parts then remove them by deleting the faces.

Final Sphere shell

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