Subject: 3D Star calculation

Hi,

I am looking for a formula that will give me a layout for a 3 dimensional 5 pointed star. I want to form it out of sheet metal, using 5 polygons and soldering them at the apex. Can you please help me with this? I would like to be able to give the formula the height of the star from the bottom two points to the top point and also how deep the star is. Thank you very much!

Sincerely,

Kent Lightcrafters, Inc.

Hi Kent

I made a cardboard model of the star. Instructions for making a cardboard star.

Kent completed his star and sent us a picture that we put in the Resource Room.

Placing the star on a sheet of paper and tracing around its edges you get the diagram below.


The center of the star is directly above A, a distance of h, at a point we'll call H. We have two more variables: b: the distance from A to B

c: the distance from A to C.

Now we want to determine the dimensions of the sheet of metal to cut out:

  

The lines HB and FG are perpendicular.

The calculations are given below.

Calculations.

The two diagrams below are side views. Notice that the angle HIJ is a right angle.

 

The diagram below is an end view.

 

If we know the ratios of h, b, and c we can simplify the formulas. In my drawings h = c = 0.4b so b = 2.5h.

Substituting into the formulas I get

Judi
Go to Math Central