Solving the Cube: A Group Theoretical Approach to Understanding the Rubik’s Cube

Publication Date

2025

Presentation Length

15 minutes

College

College of Sciences & Mathematics

Department

Math and Computer Science, Department of

Student Level

Undergraduate

Faculty Advisor

Dr. Brad Schleben

SPARK Session

2-3 Explorations in Abstract Algebra (need to go at 2:00)

Presentation Type

Talk/Oral

Summary

Understanding how to solve a rubik’s cube usually often involves finding an algorithm that consistently works. But, how many algorithms are there and can they be mathematically defined? Group Theory allows us to understand the properties of a rubik’s cube and how these properties operate.By recognizing the rubik’s cube as a Permutation Group, we can define certain properties of the cube and understand how rotating the cube’s faces changes the groups elements.

This presentation will explore the mathematical concepts of the Rubik’s Cube. This includes its group structure, how it follows permutation group properties, and the fundamental elements of the Rubik’s Cube. The fundamental elements of 8 corner cubes, 12 edges, and 6 center cubes, offer insight into how this group is going to act with specific elements. We will discuss the permutation constraints, the cube’s limitations, and how these factors affect the group’s structure. Additionally, we will be calculating the group size for the actual group and then analyze how applying certain restrictions affects its size. Ultimately, this presentation will highlight the importance of the rubik’s cube in group theory and the implications of mathematical analysis with this structure. Through the analysis, we will see how a classic puzzle can serve as an example of abstract algebra in the real world.

This document is currently not available here.

Share

COinS