A little while ago, I created a video, Engaging and Enlightening Students with Maple Visualizations, that showed a sample of Maple visualizations that would be helpful in teaching math. Doing that allowed me to get reacquainted with some of Maple's plotting features that I hadn't used for a while. As a result, I made a second instructional video for my Maple tips series, Animating a Polyhedron in Maple. 

I chose this topic because I thought it would show several features in Maple that might not be known to all users. I list them below and encourage you to try them out.

• The plots:-polyhedraplot command allows you to create a 3-D plot of a polyhedron, including one of 138 polyhedra that Maple knows about.

• The list of named polyhedra available can be obtained by calling the plots:-polyhedra_supported command.

• The viewpoint option, which allows you to create an animation by varying the viewpoint through a 3D plot, can be used to rotate the polyhedron.

• Finally, the Export feature allows you to save the plot animation as an animated GIF.

Every four years, the world comes together to watch one of the most anticipated sporting events in history: the FIFA World Cup.

Behind all the anticipation, venue planning, and media fanfare, there are many artists and researchers who devote themselves to designing a new FIFA World Cup ball to be rolled out for the public eye (pun intended).

This post presents an overview of the geometric ideas behind the design of the FIFA 2026 "Trionda" ball, using Maple to visualize and explore these concepts in depth. The ideas presented here were inspired by this Scientific American Article. For more information and facts about the 2026 Trionda ball, as well how the shape of the ball impacts play on the pitch, I suggest you check it out!

FIFA ball designs are often inspired by one of the 5 Platonic solids. A Platonic solid is a convex polyhedron with each face being the same regular polygon with the same number of faces meeting at each corner.

This year, the Trionda ball was constructed from the simplest of these shapes, the tetrahedron, consisting of 4 triangles, with 3 faces meeting at each corner. Of the five Platonic solids, this shape has the fewest faces, making it the least sphere-like. Turning such a simple polyhedron into a smooth ball is therefore a surprisingly challenging geometric problem.

So how can we turn our pointy tetrahedron into something that rolls? Rather than trying to transform the entire tetrahedron at once, we can start by redesigning a single triangular face. The goal is to create a curved triangle that will fit perfectly with three identical copies of itself while covering the surface of a sphere.