[wjhmzexi] Viewing cube faces as a grid of squares

Depict the front face of a cube as a square at the center of the display.  To the left and right are series of face views you would see if you keep turning the cube in those directions.  The series is infinite in both directions but of course repeats with a period of 4.

Above and below any given square on this central "primary" row is a column of face views, depicting the series of views you would see if you turn the cube upwards or downwards, starting with the given face as the front.  Each vertical column is again infinite and repeats with a period of 4.

Because of the geometry of the cube, horizontally neighboring squares on rows not the primary row have no obvious relationship.  The row immediately above and below the primary row happen to be different orientations of the top and bottom face.  If you rotate the cube left or right, the scene simply shifts that way.  If you rotate up or down, a more complicated change occurs off the central column.

The faces off the central row and column could be trapezoid shaped, emphasizing their connection to the faces above and below but not left and right.  The entire column tapers, as if in perspective.

One can switch from the mode with a primary row as described to an analogous mode with a primary column.

Original motivation is a UI to depict the Rubik's cube.