English: This is an animation of a 4-dimensional polytope called the w:5-cell, i.e. a hyper-tetrahedron, which has been set into a spinning motion with a constant angular velocity. It is plotted as so: the W coordinate has been squashed and replaced by a colouration, then the X-Y-Z coordinates are plotted as a conventional perspective 3D plot.

Here the polytope is exhibiting w:double rotation, where it rotates in the X-Y plane and Z-W plane simultaneously, and with different rates (Z-W rotating once per 12 seconds, and X-Y once per 9 seconds). Since there are different rates but they are fractions of each other, it takes several 'turns' to return to the original orientation.

This is part of a series of animations (these videos should loop on modern browsers):

• Simply rotating in X-Y plane
• Simply rotating in Z-W plane
• Double rotating in X-Y and Z-W planes with angular velocities in a 4:3 ratio
• Left isoclinic rotation
• Right isoclinic rotation