Gym Badges are recognition of how much you’ve interacted with particular gyms—through battling, defending, or feeding Pokémon treats.
Badges have four tiers: Basic, Bronze, Silver, and Gold. You’ll unlock new tiers as you interact more with the Gyms. As a reward for your frequent interactions with a Gym, your Badge will earn you bonus items when spinning the Photo Disc.To view your Badges:
You can also view all your Badges displayed on the globe using the Badge Map button at the bottom left corner of the Gym Badge list.
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Pokémon GO Game GUIDE