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Under the physics tab, when selecting "box" as collision shape, a green box appears around the object, which is presumibly the "collision box". Can this box be reshaped/resized, so that it becomes e.g. a bit wider than the object itself?

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You cannot move or rescale them. From the Blender manual (emphasis added):

Primitive Shapes

These are best in terms of memory/performance but do not necessarily reflect the actual shape of the object. They are calculated based on the object’s bounding box. The center of gravity is always in the middle for now. Primitive shapes can be shown in the viewport by enabling Bounds in the Object ‣ Display panel.

Use a mesh shape to get more precision:

Mesh-Based Shapes

These are calculated based on the geometry of the object so they are a better representation of the object. The center of gravity for these shapes is the object origin.

You could, however, use a parent object with a collider if you want more control.

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You can not resize the collision box itself, but you will notice that if you scale your object your collision box will scale as well. To customize the collision box:

  1. Scale your object in Edit Mode to fit the collision box.
  2. Note the scale factors on paper and take the inverse of those numbers by calculating 1/x.
  3. Then scale your Object by those Factors.

Notice that this will work perfectly for cubes, but if you want spheres you have to keep them spheres. You can not turn spheres into ellipsoids.

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