Matlab plot3 see-through element

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I am plotting the following Stewart platform in Matlab using plot3 and fill3.

The green line that I have marked in the red circle is not supposed to be visible because it is behind the top layer.

How can I make the top layer to not be see-through?

enter image description here

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Here is a link to the matlab help for the command alpha, which "sets transparency properties for objects in current axes".

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Doesn't it help to invert the order in which you plot the parts of your image? In particular, plotting/filling the upper triangle after the the circled green line?