How to apply "thickness" to a sprite in 3D space?

I would like to use a 2D sprite and give it a certain "thickness" to use it in a 3D environment. I know a sprite's appearance is only affected on two axes but I am wondering if there is a way to emulate the effect shown below.

 

As long as you don't need to turn in around all the way, you can fake this quite easily by duplicating the sprite, but rendering it a solid color, and offsetting it by some amount.