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Hyperspace structures: Exploring the fourth dimension

 

Produced by Andy Burbanks and Keith Beardmore

The hypercube
A hypercube is a 4 dimensional analogue of the cube. Details of the construction of this object are given, along with movies of a spinning hypercube.
An "inflated" hypercube
By inserting new vertices into the edges and faces of a hypercube, it may be "inflated'' to give an approximation to the hypersphere.
Hypertorus
Adding together three vectors, each rotating in 4-space with different frequencies and amplitudes, produces a trajectory along the surface of a hyper-torus.
How the models were produced
Details of the mathematics needed to model the structures, and how to turn the numbers into an animation.
Useful references
A selection of recommended books.
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