Rubik's Cube With A Twist
During my junior year of high school, a few of my close friends became infatuated with Rubik’s Cube solving. One in particular, who just recently graduated as a Mechanical Engineer as well, shared his newfound skill with a few friends from our Boy Scout troop. I had been interested in learning to solve a cube for years but until that point, I never had enough motivation to learn. During the long drive to a campsite he walked me through the solving techniques and helped me to memorize the algorithms along with his brother and another friend of ours. I practiced a lot from then on while many other scouts in my troop began to learn to solve as well, and in order to get better we would race each other and search for faster algorithms. I was personally more interested in improving my finger speed than actually changing the algorithms that I used, but I did discover a few solving shortcuts and methods of forming cool patterns along the way.
About a year after learning, I was shown a cube which was designed to open from the top to reveal a cavity meant to hold a small object inside, only once the cube was solved. That cube is officially titled the Treasure Cube, and I purchased one for myself to get a deeper understanding of its mechanisms. Around that time, I was just getting into the worlds of metal casting and 3D modeling, and I thought that it would be a great and unique project to cast each piece of the Treasure Cube from iron or some other hard castable metal. My aim was to make it much tougher than a normal plastic injection-molded cube so that it could actually be reliable for concealing an object unless the cube was solved. Every component of the treasure cube is free floating, and the pieces interact and remain locked together via tracks. If cast from a hard, tough metal, I believed that the cube would be able to withstand human attempts at breaking it to get at what’s inside.
I had originally planned to cast the cube from pieces pulled from my purchased model, however I discovered multiple loopholes in the design of the cube that I bought that would allow it to be opened from random positions without solving any part of the cube. Desiring to remove any such loopholes and armed with the 3D modeling experience that I had recently acquired using Creo Parametric in my classes, I got to work designing my own version of the treasure cube based on the product that I had purchased. I ended up with a great design that can be 3D printed and hopefully cast, which utilized newly designed keyed pieces that prevent the cube from opening at the wrong time and to the best of my knowledge, cannot be exploited. I am awaiting a time when I can afford a high-resolution SLA 3D printer capable of printing in castable wax resins so that I can begin testing different casting methods and materials to finally put this cube in my hands.
When I began modeling the Treasure Cube, I wished to improve as many of the official Treasure Cube’s shortcomings as possible to decrease the chance that my cube could be beaten by any method of opening it, through brute force or otherwise, besides solving it. Normal cubes are weak enough, with high stress concentrations occurring at internal corners that appear everywhere within the structure, but the design for the Treasure Cube does have a bit more structure to it than the conventional cube model. It supports each piece with a track rather than through the center faces being attached to a six-axis core, which leaves the entire center cavity completely open and available as a container in which to store items.
This modeling project, for me, was very educational. Creo has a plethora of tools to choose from and nearly infinite ways in which to combine them, and in this project, I played around with quite a few to get the shapes that I desired, learning creative applications of both tools that I had used before and some that I was only using for the first time along the way. I was able to successfully design a key system that would allow the cube to open only when entirely solved on the top and middle layers, which is the most that one can really do, since the bottom layer is isolated mechanically from the interface between the top and middle layers. I made sure that the keyed patterns that I came up with would only allow their exact matching counterparts to move through them, barring attempts to open the cube prematurely, which sadly was possible in the Treasure Cube sold online by exploiting certain holes in the keys. Certain parts of corner pieces, which in the official model could slide through unwanted areas causing loopholes, were barred from doing so in my improved key model.
I can still think of a few improvements that can be made to the design both to reduce stress concentration and increase surface-contact area, especially increasing the girth of some of the keyed sections to prevent brute force from breaking the cube. For now, though, I have decided that the current version is sufficient, as the adjustments that I would need to make would have little impact on the structure and would take a large amount of time to make. Once I begin printing and casting versions of this cube, I can crack down on its inadequacies.
One thing that I am quite excited for is the prospect of creating a cube based on patterns on the surfaces that only I know, rather than the traditional colors, so only I can know when it is truly solved. That way even someone learned in cube solving would be unable to open it. I could incorporate red-herring patterns or complex secondary puzzles into the surfaces as well to act as decoys.
This kind of cube is only really possible when constructed from durable materials, as the shortcut that most people would turn to for opening such a cube would almost certainly be to break it open. It’s not really meant as a practical solution to anything, just a fun party trick or even practicality disguised as a game. I’m excited about it because as for as I can tell, it’s never been done before. If it has, I’m certainly among the first to bring the idea to reality.
I mentioned that I wish to wait until I have an SLA 3D printer available to me, and I have reason for selecting SLA instead of settling for FDM printed models. The printing resolution of SLA printers has recently hit extremely high detail in consumer-available products capable of producing melt-able wax-resin prints. Previously, a large benefit of FDM printing was that its thermoplastic filament could be melted or burned away, which can be easily used in the lost-wax (or in this case plastic) method of metal casting. Now SLA printers are capable of printing with wax resins which can operate the same way, but with the benefits of unbelievably high-resolution prints when compared to FDM prints. This high resolution is especially necessary in prints as small as and with as much required detail as the components of a Rubik’s Cube, especially a Treasure Cube variant with the small keyed sections which need to mesh properly with each other with low friction. FDM-printing is incapable of producing such small sections to the tolerances necessary for my cube’s components.
I could outsource my model and have the components shipped to me, but I don’t see any fun in that and am in no hurry to finish this project, instead enjoying the process and using the extra time to consider improvements. Once I have my own SLA printer I can test my designs and make modifications to them in the real time, which is honestly the beauty of 3D printing, allowing people to prototype their designs extremely rapidly.
In order to display the structure of my Treasure Cube design, I spent a long time with Creo Parametric’s animation functions and ended up recording a full solve of my cube and the cube opening once solved. In addition, I produced videos of the structure revolving with only certain components visible to give further insight into the internal structure of the model. Creo Parametric 3 has no option to record an animation of a cross-section slice being moved along a certain direction, however I wanted to display such a cross-sectional view of the entire cube. To get around this problem, I developed a computer macro that repeated a large chain of steps in Creo to adjust the slice location, take a screenshot of the window, and save it to a new PNG image. I set this to run for a few hours and captured 1200 images with which I constructed my cross-section slice video, emphasizing the differences between pieces of the cube by changing their material colors.
A friend of mine asked me to write down instructions to help her learn how to solve a cube in 2018, so I wrote a very comprehensive set of instructions detailing the steps necessary for a reliable brute force method of solving of a 3x3 cube. I am familiar with many shortcuts and when they should be used that were not detailed in this instruction set. I decided to keep them out to prevent confusion, to allow the one solving to learn the absolute basic form of the algorithms, and hopefully, help them to visualize what goes on within the cube when these algorithms are performed.
I truly believe that much of the fun of solving these puzzles lies in finding certain solutions yourself, whether they be shortcuts or ways to form interesting patterns. Cube-solving is an art that I will never forget how to perform. It is a great pass-time that keeps the mind nimble, improves hand motor function, and is always a neat party trick.