A STEM Project: A Square Cube Vase: Where Math Becomes Art

A Square Cube Vase: Where Math Becomes Art

Have you ever wondered what happens when geometry, code, and creativity come together in a single project? This is the story of a piece that shows how math can become art when you blend digital tools with the love of making things by hand.

Designing the Cube Vase 

Using Silhouette Studio and TurtleStitch, I created a cube-shaped vase lined with vellum and decorated it with delicate, lacy floral cutouts. I arranged twelve layered paper flowers on stems, each designed in code and cut with precision with the Silhouette Cameo. The result is a vase that proves papercrafting and coding belong together. 

Cut Files 

You need an electronic cutting machine for cutting the files.  The .Studio file is for the Silhouette machine and the SVG file for the Cricut machine.

Here is the .Studio file. 

https://drive.google.com/file/d/17vfuYHk_q6J65TuIA0UM4ZSHgSPvVLxL/view?usp=sharing

Here is the SVG. The file extends beyond the viewable area.  Zoom out to see the entire file.

https://drive.google.com/file/d/1Klufu3oJgE0vyh-GbrUg0tUoOdpocfSj/view?usp=sharing

Creating Three-Dimensional Flowers 

I coded two Turtlestitch programs to make the flowers. The Petal Block Flower and Petal Arc Block Flower. 

The  Petal Block Flower program uses a custom 'petal' block that allows you to generate complete flowers with just two inputs:

• radius - controls the arc size

• degrees - sets the arc angle

Each petal uses two symmetrical arcs connected by a (180° - degrees) turn which is the key to maintaining perfect symmetry.

 This works because 180° represents a straight line, causing the turtle to flip across the centerline and mirror the first arc. The pattern then repeats around the circle with petals spaced using 360° ÷ number of petals.  If you replaced 180° with a different value (for example, 120°), you would get a lopsided, asymmetrical petal. 

The Petal Arc Block Flower program takes into account this anomaly. The formula to compensate for the difference is:

final turn = 360° ÷ number of petals − ( 2 × arc angle) + inner turn

This formula accounts for three things:

• The total angle the turtle turns while drawing both arcs.

• The sharp turn between the two arcs.

• The final adjustment needed to evenly space the petals around the circle.

When the turtle's rotation doesn't complete a full circle, adding 360° ensures it's properly oriented for the next petal. This technique maintains perfect symmetry regardless of your petal design.

Assembling The Vase

To make the vase, glue the vellum to the inside of the box sides. Glue the side tabs of the vase together to form a square. Bend the tabs of the bottom of the vase at a right angle.  Apply glue to the tabs and slide the bottom into the vase body.

To make the stems,  fold and glue one half of each side together at a 90-degree angle to form an X.  The two ply stems offer stability for the flowers.

The right angled stems are inserted into the base and the tabs were glued as shown.  The base of the stems is glued to the inside of the cube.  The inserted tabs provide a lip around the cube.

The tops of the stems are flared so that the flowers can be glued on to a secure base.
Attach each flower to a paper stem.

Assembling Three-Dimensional Flowers 

I made twelve three-dimensional flowers to accompany the vase. Each flower was cut in graduated sizes so the largest layers formed the base and the smallest topped the bloom for a full, sculptural look. 

To assemble: Stack the flower layers from largest to smallest, securing them in the center. 
Combine the two TurtleStitch flower designs to create visual variety.

Arrange the flowers around the vase in a natural, pleasing composition. Have fun mixing shapes, heights, and colors so the bouquet looks interesting from every angle.

The Math Behind the Flowers

This project was powered by math at every stage, using both TurtleStitch and Silhouette software: 

• Rotation and Repetition: Petals repeat evenly around a central point, each rotated by a precise angle (e.g., 60° for six petals). 
•  Arc Geometry: Arcs are defined by radius and angle to create smooth curves. 
• Symmetry and Tessellation: Dividing the circle evenly produces perfect balance. 

The result is more than just a container for flowers. It’s a unique vase, part sculpture, part floral arrangement, and completely inspired by the possibilities of math and digital papercrafting. This project shows that math can become art in your hands and can be displayed as a testament to the beauty of mathematics.