Hummer 2006 H3 Owner's Manual page 346

The spare tire is attached to the outside of the
swing-gate. To remove the spare tire, do the following:
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1. Remove the center cap
by placing the flat end
of the wheel wrench
in the slot on the wheel
and gently pry the
center cap out.
3. Pull off and gently lower the spare tire to the
ground. Set it next to the flat tire.
In order to remove the spare tire, you may need
someone to assist you.
2. Use the wheel wrench
to remove the wheel
nuts securing the
spare tire.
If your vehicle has
locking lug nuts,
the key is supplied
in the tool bag.
Use the key along
with the wheel wrench
to remove the wheel
nuts from the tire.