May 26, 2014

The quaternion group {1,i,j,k,-1,-i,-j,-k} is a beautiful group of order eight. It didn't have a physical representation because the object should be 4-dimensional. But has the quaternion group ever appeared as the symmetry group of an object? The answer is yes. In order to visualize the symmetries of the quaternion group, mathematician Henry Segerman, sculptor Will Segerman and mathemusician Vi Hart have designed a four-dimensional object, a hypercube, and put a monkey at the center of each of the eight cubes.

To visualize a 3D object 2-dimensionally, one method is to make shadow on a wall using a light source. Segerman and Vi Hart have used a similar projection technique and magic of 3D printing to make 3D prints of projections of 4-dimensional objects. They call it "Nothing Is More Fun than a Hypercube of Monkeys."

The sculpture is printed in PA 2200 plastic using Selective Laser Sintering Technology. Because the projection distorts size, so some of the moneys, even they are all the same size in 4 dimensions, look larger than the others.

You can watch the video below Segerman gives a talk about the technique of how to make sculptures of 4D things. Or read their paper The Quaternion Group as a Symmetry Group, on the ArXiv.


Posted in 3D Printing Applications


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