![]() ![]() Spheres and Truncated ConesĪfter finding the coordinates for the corners of the tesseract for any \(\theta\) value, I can construct the object with spheres and cylinders for the vertices and edges. If you understand these concepts as they are applied to 3D geometry, making the analogy to 4D space is straightforward. I can do this repeatedly for many values of \(\theta\) and model all of them to visualize the tesseract as it rotates in 4D space. Those are the 3D dimensions of the tesseract that will be modeled in Rhino and eventually 3D printed. Each result can then be projected down to 3 dimensions. Then multiply each by the appropriate 4D rotation matrix and translate in the positive \(v\) direction away from the origin. These are fundamental to my thinking this through and understanding what I am building. I can simplify my workload by considering this in my design.Įqually important are the sketches of the equations behind this project. Also, there is symmetry in that rotations between 45 and 90 degrees are mirror images of rotations between 0 and 45 degrees. It is easier to think about them after doing the math, but even then, it is not easy drawing a 4D object on a 2D piece of paper.Ī rotating tesseract will repeat itself after a 90 degree rotation. My drawings of a tesseract are terrible because they are almost impossible to visualize. Designing a Tesseractįirst, I started with some sketches. This project was inspired in part by the book Visualizing Mathematics with 3D Printing. These 3D printed tesseracts can be assembled in a stop motion animation to show what the tesseract looks like as it rotates around 4D space. Using math and 3D printing, I can create multiple versions of a rotating tesseract. Similarly, a rotating tesseract can help us understand what they are like. ![]() ![]() A 2D being cannot understand, visualize, or fully experience a cube, but as a cube rotates around, they can gain a better understanding of what the structure is like. Tesseracts can interact with a 3D world in a way that is similar to a cube interacting with a 2D world. They are theoretical structures that can be understood mathematically. Tesseracts are challenging for 3D beings to visualize and understand. It is analogous to a cube in our 3D world. A tesseract, or hypercube, is a 4 dimensional cube. To explore this, I will analyze and study a tesseract. I am interested in using 3D printing to model and visualize mathematics. ![]()
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