Tesseract Assembly

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This quick movie shows how to build a tesseract from a point by extrusion. We extrude a point to become a line segment, then extrude the line segment to become a square, and the square to become a cube, then (finally) the cube to become a tesseract.

The tesseract has eight cubes: the original cube, the cube at the other end of the final extrusion, and six cubes that connect the two. Many of the cubes appear heavily distorted, but you should be able to identify them all.

To aid visualization, I also render the cube in color space, which is a 3-D space so only one projection is required. The four directions are rendered chromatically as (Red, Green, Blue, White).

The 4-D perspective uses a fairly conventional dual projection - both out-of-plane axes are projected obliquely up and to the right, at two different angles. The projection isn't orthographic - I included both foreshortening and distance scaling, to help visualize what's going on. You might also like the companion video (), which shows rotation of the tesseract about all of its major axes.