Describe the shape of projection of vertices (vector positions of a cube) onto a 2D plane from a source (position vector)?

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I am having trouble with this. I can manually calculate every single projection point onto the z=0 plane from deriving vector equations to get to the z plane for each vertices. From this I can then plot all these coordinates to find the shape. Is there a better/faster method as this question shouldn't take long. Many thanks

The question for context is here Here is my method

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You should get a hexagon a rectangle or a square.

$(\frac 14, \frac 54), (\frac 14, \frac 94),(\frac 54, \frac 54),(\frac 54, \frac 94), (-\frac 12, \frac 32),(-\frac 12, \frac 52),(\frac 32, \frac 52),(\frac 12, \frac 32)$

How do you get these.

$P_n - \lambda L$ and find $\lambda$ such that the $z$ component equals $0.$

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