Finding symmetries both geometrically and analytically. PLEASE HELP

[JohnMcBetty]

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.

 

[micromass]

You can start by sketching the figure. Now, what symmetries can you see in the figure?

 

[JohnMcBetty]

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).

 

[JohnMcBetty]

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

 

[Deveno]

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