Document Type


Peer Reviewed


Publication Date


Scholarship Domain(s)

Scholarship of Discovery


Polyforms are created by taking squares, equilateral triangles, and regular hexagons and placing them side by side to generate larger shapes. This project addressed three-dimensional polyforms and focused on cubes. I investigated the probabilities of certain shape outcomes to discover what these probabilities could tell us about the polyforms’ characteristics and vice versa. From my findings, I was able to derive a formula for the probability of two different polyform patterns which add to a third formula found prior to my research. In addition, I found the probability that 8 cubes randomly attached together one by one would form a 2x2x2 cube. Finally, I discovered a strong correlation between the probability of a polyform and its number of exposed edges, and I noticed a possible relationship between a polyform’s probability and its graph representation.


Honors Capstone Project completed in 2012 for Olivet Nazarene University.