A STEM Project: How to Make a Slice Form Sphere Using the Silhouette Software

A slice form sphere is a dazzling spectacle. A two dimensional object, paper, is transformed into a three dimensional object by sliding slices of the form into one another. 

A slice from sphere can also lie flat.

In this blog posting, I will explain how to create a slice form circle with the Silhouette software and then use the Pythagorean theorem to create the other circles spaced across the sphere.

How to Make a Custom Sphere

- Make the Center Slice

The slices in a slice form can not be enlarged or decreased once the sphere is made because the paper slits need to accommodate the thickness of a piece of paper.  Each slit is 0.02 inches wide. Once you determine the size of the sphere, you need to determine the number of slices.  The number of slices will always be an odd number. The center slice and the corresponding slices on either side of the center. (Only three slices need to be designed.  One center slice and the two slices on one side of the sphere. Once these two slices are designed, they can be duplicated for the other side of the sphere.) I determined that five slices total was a good number because it would visually allow you to see the scenery (my goal is to make a diorama) but still give a nice structure. 

Using the Silhouette software, draw a circle the size of your sphere. In this example, I am going to make a four inch sphere.  Center the circle to the center of the page.  

Draw a vertical rectangle the length of your sphere, 4 inches by the width of a slice, .02 inches. 

Using the Replicate function, Number of Copies will be 4 (one less than the number of slices).  Custom Position each Copy of this vertical rectangle in the X offset by 0.5 inches. The slices will be 0.5 inches apart.

Make Compound path of the vertical rectangles and center them to the page.  These vertical rectangles will become the slices. (At this point, you can change the spacing of the slices, but the calculations will be different then what I have given.)

Move the vertical rectangles from the center of the page.  Internal offset the 4 inch circle by .35 inches to create a circle frame. 

The center of this circle frame is found by doing a .175 inch internal offset of the 4 inch circle. This center location is the stopping point when the opposite slice is slid into one another. 

Align Center the vertical rectangles to the top of the circle. Release the compound path of the vertical rectangles and move each individual rectangle downward so that it slightly overlaps the center of the circle frame.

I used the downward arrow key to move each vertical rectangle. Make a copy of this screen for later use;  either on the same page or to another file. I like to copy it to a temporary file because I like to use the Undo function for mistakes and it is easier if things are not complicated with multiple revisions.

Delete the center of the circle frame.  Make a compound path of just the circle frame.  

Select all of the vertical rectangles and make them a compound path. Copy it to memory using Edit Copy.

Select the vertical rectangles first and then the circle frame.  In the modify window, Subtract the vertical rectangles from the circle frame.

The result will be outer slice of the slice form circle.  Rotate this image 180 degrees in the Object window.

The image has been rotated 180 degrees. Go to the Edit window and Paste in Front.

The vertical rectangles will be placed in the same exact location as the last time. Select the vertical rectangles and then the circle frame as before.  

In the Modify window, Subtract the vertical rectangles from the circle frame.

The result will be one of the slices of the slice form. This is the outer slice because the slits are on the outer side.  The inner side slice needs to be made next.

Retrieve the the file that you saved earlier to make the inner slice.

Select the vertical rectangles and make them smaller so that they will fit inside the circle, as shown above. Group them together in the object window to move to the inside of the circle and Align Center the vertical rectangles as before.

 Ungroup the vertical rectangles. With the up arrow key, move the vertical rectangles individually upward so that it slightly overlaps the center of the circle frame.

Delete the center of the circle frame. Select all of the vertical rectangles and make them a compound path. Copy it to memory using Edit Copy.

Select the vertical rectangles first and then the circle frame. 

In the modify window, Subtract the vertical rectangles from the circle frame.

The result will be one half of the slice form circle.  Rotate this image 180 degrees in the Object window.

The image has been rotated 180 degrees. Go to the Edit window and Paste in Front.The vertical rectangles will be placed in the same exact location as the last time. Select the vertical rectangles and then the circle frame as before.  In the Modify window, Subtract the vertical rectangles from the circle frame.

 The result will be the corresponding slice. This is the inner slice because the slit is on the inner side. 

A pair of slices, the outer slice and inner slice, complete the center slices for the slice form sphere.

- Determine the Size of the Other Two Slices with the Pythagorean theorem

The two smaller circles are equally spaced from the center circle. Here is the PDF of the calculations if you want to print them out. 

https://drive.google.com/file/d/1FGSB1KT8mVWJTcZw19KHub6BCcLHu8nj/view?usp=sharing

The size of two smaller circles will be 3.872 inches and 3.464 inches respectively.

- Repeat "Make the Center Slice" instructions with a 3.872 inch circle. 

   The offsets and all of the other instructions are the same for making an outer and an inner slice.

- Repeat "Make the Center Slice" instructions with a 3.464 inch circle.

 The offsets and all of the other instructions are the same for making an outer and an inner slice.

  

Once completed, the slice form circles should look as above.

Here is the .Studio file that I created for this blog post and the next post.

https://drive.google.com/file/d/1l6ekHJjy63DM-Bpe_JUEY1HtRslktYE1/view?usp=sharing

I used 65 lb. Neenah metallic card stock from Office Depot to make this slice form.

The interior of the slice form sphere is an area where a diorama can be created. In my next blog posting https://papercraftetc.blogspot.com/2020/10/a-stem-project-adding-scenery-to-slice.html, I will explain how to use these slice form circles to make a slice form sphere with a diorama inside.

Assembling a Slice Form Sphere

Please note: The center slice (four inch circle) only needs to be cut out once.  All of the other circles need to be cut out twice.

Arrange the slices according to size and slit location (outer or inner slits).

Take the the two largest circles and insert the slits into one another.

Insert the slits (top and bottom) of the next largest slices on either side of the center. I recommend doing the  outer slices first (slits are on the outside of the circle).

Insert the slits for the smallest outer circles.

Insert the slits for the next largest inner circles. The inner slices are slid into place by first doing all of the top slits and then inserting the bottom slits. This will take some time so go slowly as the slits like to slide out by themselves.

Insert the slits for the smallest inner circles.

Completed Slice Form Sphere