Projections of the Four-Cube

rotate in coordinate plane:

w-x

0.5

w-y

0.5

w-z

0.5

opacities of opposite cubes:

x

0.25

y

0.25

z

0.25

w

0.25

axes

Rotate a four-dimensional cube and project it into three-dimensional graphics. The rotation is the composite of rotations in the w-x, w-y, and w-z planes, in that order. Opposite cubes (3-cells) of the hypercube have similar colors. Play with the opacity to see how the hypercube is bounded by eight cubes.