Rotating a Hypercube in Four Dimensions with Eight Spaced Cubes

opacity

0.4

spacing of cubes

1

stereographic projection

1

rotations in four dimensions

fixedplane

control

angle ofrotation

W-X

0

W-Y

0

W-Z

0

X-Y

0

X-Z

0

Y-Y

0

reset rotations

(stop animations first)

Initialization timed out



This Demonstration gives a variety of animated rotations of a hypercube in four dimensions with eight spaced cubes projected onto three dimensions. An axis (set of fixed points) of a four-dimensional rotation is a plane. As a simple example, stop the animation and set all the angles to zero. Drag the first slider; this rotates the hypercube without distortion about the

W

-

X

plane, which in three dimensions represents a rotation about the

X

axis.