# Pumpkin Jack-o’-lantern Sliceform

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I was recently introduced to a new-to-me form of math art known as the sliceform. Since Halloween is next week, the first sliceform that I tackled was a pumpkin or jack-o’-lantern sliceform. If I can say so myself, it looks pretty cool sitting on my desk next to my Columbus Cube tower.

## What are Sliceforms?

I discovered the mathematical art of sliceforms from the twitter account of María García Monera, a math teacher from Spain.

How could I not want to learn more after seeing this awesome looking jack-o-lantern? I didn’t know what sliceform was, but I knew that I needed to find out.

I soon discovered that María has an entire webpage dedicated to sliceforms with free templates to print!

Sliceforms are models made from intersecting parallel planes which slot together to form a 3D shape with a very interesting characteristic that I’ll mention in a minute.

Don’t these look AWESOME?

Each of these 3D sliceforms folds completely flat!

I was very thankful to discover that María has filmed a video to explain the basic process of assembling a sliceform using the templates provided on her website.

If you don’t believe what I said about the models folding flat, check out her video for a demonstration of this awesome property of sliceforms! Or, you can check out my very unedited video of my pumpkin sliceform model below.

## Building the Pumpkin/Jackolantern Sliceform

I began my sliceform building process by printing María’s pumpkin (calabaza) sliceform template on Orange Astrobrights cardstock.

UPDATE: María has also shared a template that creates a sphere for the pumpkin with only 10 pieces. This would be much easier for students to assemble in a single class period!

Up next, I spent some quality time with my scissors cutting out all of the circle templates.

Arrange them in size from largest to smallest.

Cut on the lines marked on each template.

When I did this step, I missed a piece of CRUCIAL information on María’s website. Instead of just cutting on each line, I should have made two cuts on each side of the line so that a small piece of the cardstock could be removed.

Skipping this step explains why I had such difficulty getting my pieces to slide together easily!

Lay out all of the circle templates. Note: each piece is either an A or a B piece. This is based on whether the cuts are facing up or down on the model.

Take the two largest circle templates and put them together so that they intersect perpendicularly.

Follow the building instructions provided in the video linked above. Basically, you will add two pieces going one direction, flip the model over, and add two pieces going the other direction. Repeat the process until the entire model is assembled.

I found myself having lots of trouble getting the pieces to slide together. This is most likely due to my overlooking the cutting instructions I shared above.

The thing that seemed to help me the most was inserting a sheet of paper into the model where my next piece would go before trying to put the next circle template into the model.

Finally, we’re making progress!

Here’s what it will look like once the circle templates are assembled.

Of course, I had to test and see if it would indeed fold flat. It worked!

The last step is to decorate your jack-o’-lantern. The template came with decorations. I originally planned on cutting them out and tracing them on black construction paper, but I ended up just cutting them out of the orange cardstock and coloring it black.