Finding symmetries both geometrically and analytically. PLEASE HELP

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Discussion Overview

The discussion revolves around identifying the symmetries of a double square pyramid, specifically focusing on both geometric and analytical approaches. Participants explore the challenges of visualizing and understanding the 3D structure and its symmetries.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant suggests starting with a sketch of the double square pyramid to identify visible symmetries.
  • Another participant expresses difficulty in drawing 3D shapes, particularly with three coordinates.
  • One participant proposes that there may be a rotation symmetry of order 3 due to the pyramid structure.
  • Another participant counters that the specific positions of the vertices E and F at (0,0,1) and (0,0,-1) limit the possible symmetries, implying that typical rotational symmetries may not apply.

Areas of Agreement / Disagreement

Participants express differing views on the existence and nature of symmetries in the double square pyramid, indicating that the discussion remains unresolved with multiple competing perspectives.

Contextual Notes

Participants note challenges related to visualizing 3D shapes and the implications of vertex positioning on symmetry, but do not resolve these issues.

JohnMcBetty
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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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