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Question: How to overlay an image on a 3D surface? (Texture mapping?)

I want to make a 3D image of a US one cent coin (a penny).  To produce one face of the penny I thought of doing

plot3d(0, y=-sqrt(1-x^2)..sqrt(1-x^2), x=-1..1, image="penny.png");

but this distorts the circular image into something that's not quite circular:

What is a better way of doing that?

 

 

Here is the image penny.png that I used: 

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