Calabi-Yau manifolds are an essential ingredient of compactification scenarios in ten-dimensional string theories, where they describe the wrapped up shape of 6 of the 10 spacetime dimensions.
More info on this particular visualization, which shows a "sliceā through a six-dimensional manifold, can be found here: http://members.wolfram.com/jeffb/visualization/stringtheory2.shtml
Visualization: Jeff Bryant
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