Finding symmetries both geometrically and analytically. PLEASE HELP

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In summary, the conversation discusses finding symmetries of a double square pyramid. A coordinate system is introduced and the vertices of the pyramid are listed. The task is to identify the symmetries both geometrically and analytically. The difficulty of drawing 3D shapes is mentioned, but the assumption is that there would be some kind of rotation with cycle 3. However, the vertices at (0,0,1) and (0,0,-1) prevent certain symmetries from being present.
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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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  • #2


You can start by sketching the figure. Now, what symmetries can you see in the figure?
 
  • #3


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).
 
  • #4


I would assume there would some kind of rotation with cycle 3, being that it is a pyramid.
 
  • #5


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

Related to Finding symmetries both geometrically and analytically. PLEASE HELP

1. What is the difference between geometric and analytic symmetries?

Geometric symmetries refer to patterns or structures that are visually identical when rotated, reflected, or translated. Analytic symmetries, on the other hand, involve mathematical equations and functions that are symmetric about a certain point or axis.

2. How do you find geometric symmetries?

To find geometric symmetries, you can use techniques such as drawing lines of symmetry, using a symmetry template, or using the rotation or reflection method. These methods help identify the type and number of symmetries in a given shape or pattern.

3. What is the process for finding analytic symmetries?

To find analytic symmetries, you need to analyze the equation or function and determine if it is symmetric about the x-axis, y-axis, or origin. You can also use algebraic techniques, such as substituting x and y values and checking for symmetry.

4. Can a shape have both geometric and analytic symmetries?

Yes, a shape can have both geometric and analytic symmetries. For example, a circle has an infinite number of geometric symmetries (rotational symmetry) and is also symmetric about its center (analytic symmetry).

5. How are symmetries useful in science?

Symmetries play a crucial role in science, particularly in fields such as physics, chemistry, and biology. They help us understand the fundamental laws and principles of nature and make predictions about the behavior of systems. Symmetries also aid in the design and development of new materials, structures, and technologies.

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