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Finding symmetries both geometrically and analytically. PLEASE HELP

by JohnMcBetty
Tags: abstract, algebra, coordinate, pyramid, symmetry
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JohnMcBetty
#1
Apr1-11, 02:32 PM
P: 12
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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micromass
#2
Apr1-11, 04:31 PM
Mentor
micromass's Avatar
P: 18,019
You can start by sketching the figure. Now, what symmetries can you see in the figure?
JohnMcBetty
#3
Apr2-11, 10:25 AM
P: 12
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
#4
Apr2-11, 10:46 AM
P: 12
Finding symmetries both geometrically and analytically. PLEASE HELP

I would assume there would some kind of rotation with cycle 3, being that it is a pyramid.
Deveno
#5
Apr6-11, 09:17 AM
Sci Advisor
P: 906
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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