SchoolArts Room

Playing with Paper Icosahedrons

By Kristin Ponden, posted on Oct 26, 2021

A little-known fact about me is that I was the captain of my high-school math team. So, it should come as no surprise that I love finding ways to incorporate mathematical concepts into my art lessons. One such project that has been incredibly successful over the years is printed paper icosahedrons, which give my seventh-grade students the opportunity to work in a variety of media to create a 3D sculpture.

middle school art lesson, paper icosahedrons, student art
Left: A student carves their pattern. Right: The printmaking process.
middle school art lesson, paper icosahedrons, student art
Left: Robert. Right: Alyssa, grade seven, assembles her icosahedron.
middle school art lesson, paper icosahedrons, student art
Right: Madeline.
middle school art lesson, paper icosahedrons, student art
Left: Bea. Right: Elliott.
middle school art lesson, paper icosahedrons, student art
middle school art lesson, paper icosahedrons, student art
middle school art lesson, paper icosahedrons, student art
middle school art lesson, paper icosahedrons, student art
Left: Ryley. Right: Sabine.

An icosahedron is a geometrical figure that consists of twenty equilateral triangle-shaped sides. Students who are into role-playing games might recognize it as the D20, the signature die of Dungeons and Dragons. Icosahedrons can also be seen in the molecular composition of certain viruses, and Buckminster Fuller famously subdivided it into the geodesic dome, the iconic shape that welcomes visitors to Disney’s Epcot Center. This shape is fun to play with and creates the perfect blank slate for this dimensional printmaking project.

Essential Questions
I begin the lesson by posing several essential questions to help frame students’ learning. I want students to think broadly about the concepts they are learning and how they have implications beyond the immediate product they are creating. Questions include:
What is the benefit of using geometric concepts to create patterns?
Why should we consider the intersections between math and art?
How can technology make certain artistic processes easier for artists?

Op-Art Inspiration
I introduce students to the Op Art movement and artists such as Bridget Riley, Victor Vasarely, and Jesús Rafael Soto, who paved the way for contemporary artists such as Tofer Chin and Manil Gupta. Their optical illusions present the inspiration for the prints students will produce. Each student uses a block of printmaking material cut into an equilateral triangle. They can carve up to two different designs (one on each side).

Planning and Envisioning
The most complex aspect of this project is the planning and envisioning that is involved. I have students sketch their ideas for their finished icosahedrons in their sketchbooks so they can plan out their printed designs, colors, and cut-out shapes, and how everything will fit together. This step is integral to ensure that students understand the process and have a clear vision for the end product.

Designing and Cutting Shapes
To create the intricate cut-out shapes that extend from the icosahedron, I have students work with a free web-based design program called Vectr. This program is user-friendly and easy to learn, so students can focus on their designs rather than the technical aspects of the software. Similar vector-based software can also be used, and if necessary, this step can be done by hand, but the complexity of the designs might have to be limited.

Some students create more than one design, while others take a more symmetrical approach. They share their designs with me and let me know how many pieces they would like to have cut out. I use a computer-controlled cutting machine (Cricut Maker) to cut their designs on 80# white paper.

The Printing Process
I provide students with a blank icosahedron template that I cut out beforehand. Once they have their designs carved and their pieces cut out, they can start the printing process. I encourage students to think ahead and refer to their original sketches to help them understand how they need to print to achieve their ideas. An assembled icosahedron is helpful to show how the pieces eventually fit together. I remind them that five triangles come together at both the top and bottom and then wrap around the middle.

Integrating Math and Visual Arts
Students get enormous satisfaction from assembling the finished sculptures and seeing them hang from the ceiling of the art room. I love offering them a glimpse into the ways that mathematics and visual arts complement each other, and to let them flex their creative muscles to create incredibly complex designs. I always encourage new ideas, and I am thrilled when students figure out unique solutions to this project and try things that go beyond my initial instructions.

Each year, my students surprise me with their sculptures, just as I surprise them with my love of math. It is important to me to show them that the subjects they study in school are not mutually exclusive, but rather that they naturally integrate in ways that are both inspiring and complex.

Krissy Ponden is visual arts department chair at the Unquowa School in Fairfield, Connecticut.

National Standard
Connecting: Relating artistic ideas and work with personal meaning and external context.

The Unquowa School
Icosahedrons Template

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