Finding symmetries both geometrically and analytically. PLEASE HELP

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Finding symmetries both geometrically and analytically. PLEASE HELP!

I have found this question and not sure where to begin in terms of solving it. PLEASE HELP!

Consider a double square pyramid . Introduce a coordinate P system so that the
vertices of P are:

A=(2,0,0)
B=(0,2,0)
C=(-2,0,0)
D=(0,-2,0)
E=(0,0,1)
F=(0,0,-1)

List the symmetries of P. Do this both geometrically and analytically.
 
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You can start by sketching the figure. Now, what symmetries can you see in the figure?
 


I tried drawing it out, but I just have a lot of trouble with 3D shapes. I have trouble drawing figures with 3 coordinates (x,y,z).
 


I would assume there would some kind of rotation with cycle 3, being that it is a pyramid.
 


normally, there would be. but the vertices at E and F being at (0,0,1) and (0,0,-1) preclude those symmetries.
 

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