Where is my avatar in inventory

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While this may sound strange to you, it's located under "Body Parts" or even "Clothing", usually under a folder called "Male/Female Shape & Clothing", although you might have changed its name. Weirdly enough, avatars are just nice textures on top of a polygon mesh, and changing the avatar's looks is just a question of dragging things like shape, skin, eyes and hair on top of yourself!

BTW, you can have as many different avatars (male, female or otherwise) as you wish, there is no limit.