Creating a 3D Pentagram: Find Equation for Sheetmetal

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Discussion Overview

The discussion revolves around finding an equation or method for creating 2D pentagrams from sheet metal, with a focus on how to adjust dimensions while maintaining the correct angles and shapes. Participants explore the challenges of scaling the design and the geometry involved in constructing a 3D version of a pentagram.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant seeks an equation to create various sizes of 2D pentagrams from sheet metal.
  • Another participant questions the definition of a 3D pentagram, noting that they are only familiar with the 2D version.
  • Concerns are raised about how changing the size of the pentagram affects the angles, indicating a need for further elaboration on the design process.
  • A participant describes the process of cutting diamond shapes and bending them, but struggles with how to adjust measurements for different sizes while maintaining the correct angles.
  • There is a suggestion to provide a diagram or photo to clarify the design, with a focus on the angles involved in creating a true pentagram versus a simple star shape.
  • Discussion includes the specifics of how the diamonds are constructed, including the need for a central bend to create a raised effect.
  • One participant proposes a rough trial method for scaling the diamonds, suggesting to increase the width slightly to adjust the inner angle.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the geometry of pentagrams and the implications of scaling. There is no consensus on a specific method or equation for creating the pentagrams, and the discussion remains unresolved regarding the best approach to maintain the correct angles while resizing.

Contextual Notes

Participants have not fully defined the assumptions regarding the angles and dimensions necessary for constructing the pentagram shapes, leading to potential misunderstandings about the geometric relationships involved.

lookingdown
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Im looking to find some type of equation that i can plug numbers into for making a number of different sized 2-D pentagrams out of sheetmetal?
 
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lookingdown said:
my mistake.. I am running into the problem that if i change the size, all my angles change.
I think you're going to need to elaborate.
 
DaveC426913 said:
I think you're going to need to elaborate.

i am making 2 dimensional pentagrams.. i am running into the problem that if I make one to a certain size I can't just enlarge the pieces to make one bigger.. ??
 
see I am basically cutting out diamond shapes and breaking them in a metal break to put an angle on the diamonds running the length of them,, but where they all connect at they have to be a certain angle and I am not sure how to upsize or downsize measurements to make this work out
 
Can you supply a diagram or a photo?

These diamonds, are you basically making 5 of them and joining them into a star pattern? The central angle would be 360/5 = 72 degrees. It is not the same as the angle at the outer point, which will be different if you want them to be true pentagrams, as opposed to simple stars.

See attached samples of different five-sided shapes.

I suspect you are trying to construct #1. But if you use true diamond shapes (opposite angles are equal), you will end up with #2.
 

Attachments

  • PF20091217pentagrams.gif
    PF20091217pentagrams.gif
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they are not flat they are raised in the middle.. see I am putting a bend right down the middle of the center of the diamond so it sticks up in the middle..
 
lookingdown said:
they are not flat they are raised in the middle.. see I am putting a bend right down the middle of the center of the diamond so it sticks up in the middle..
Ah. But otherwise, does it look like #1 in my diagram?

How much is it suppsoed to bend up?
 
  • #10
yes it does look like that diagram it doesn't matterjust nothing with too much of a pitch
 
  • #11
lookingdown said:
yes it does look like that diagram it doesn't matterjust nothing with too much of a pitch

Is the centre raised with the points set back? Or are the centre and points in the same plane? i.e. if you lie it flat on the table, will the centre touch the table?


[ EDIT: Nevermind, the centre and points can't all touch ]

If you want to simply do a rough trial, then try this:


Take one of the diamonds I diagrammed.
On paper, scale it up to the size you want.
Add about 5% to its width (i.e. if your diamond is 10" from side-to-side, make it about 10.5")

This should get you a diamond whose inner angle is a now little more than 72 degrees. You will need to crimp it down the middle to make it 72 degrees, at which point 5 of them will complete a circle.
 
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  • #12
center raised out
 

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