Take Model 7. On one side of it there is a Dark-blue square, which is
identical with the Dark-blue square of Model 1. Placing it so that it
coincides with 1 by this square line for line, we see that the square
nearest to us is Burnt-sienna, the same as the near square on Model 2.
Hence this cube is a model of what the Dark-blue square traces on moving
in the unknown direction. Here the unknown direction coincides with the
negative away direction. In fact, to see this cube, we have been obliged
to suppose the Blue line turned into the unknown direction, for we
cannot look at more than three of these rectangular lines at once in our
space, and in this Model 7 we have the Brown, Orange, and Stone lines.
The faces, lines, and points of Cube 7 can be identified by the
following list.
The Dark-blue square traces a Dark-stone cube (whose interior is
rendered invisible by the bounding squares), and ends in a Burnt-sienna
square.
Each Line traces a Square and ends in a Line.
The Orange line} {Azure square} and{Leaf-green line
„ Brown „ }traces{Yellow „ }ends{Dull-blue „
„ French-grey „ } an {Yellow-green „ } in {Dark-pink „
„ Reddish „ } {Ochre „ } a {Brown-green „.
Each Point traces a Line and ends in a Point.
The Gold point } {Stone line } and{Silver point
„ Fawn „ }traces{Smoke „ }ends{Turquoise „
„ Light-blue „ } a {Rich-red „ } in {Quaker-green „
„ Dull-purple „ } {Green-blue „ } a {Peacock-blue „.
If we now take Model 3, we see that it has a Black square uppermost, and
has Blue and Orange lines. Hence, it evidently proceeds from the Black
square in Model 1; and it has in it Blue and Orange lines, which proceed
from the Gold point. But besides these, it has running downwards a Stone
line. The line wanting is the Brown line, and, as in the other cases,
when one of the three lines of Model 1 turns out into the unknown
direction, the Stone line turns into the direction opposite to that from
which the line has turned. Take this Model 3 and place it underneath
Model 1, raising the latter so that the Black squares on the two
coincide line for line. Then we see what would come into our view if the
Brown line were to turn into the unknown direction, and the Stone line
come into our space downwards. Looking at this cube, we see that the
following parts of the tessaract have been generated.
The Black square traces a Brick-red cube (invisible because covered by
its own sides and edges), and ends in a Bright-green square.
Each Line traces a Square and ends in a Line.
The Orange line} {Azure square } and{Leaf-green line
„ Crimson „ }traces{Rose „ }ends{Dull-green „
„ Green-grey „ } an {Sea-blue „ } in {Dark-purple „
„ Blue „ } {Light-brown „ } a {Purple-brown „.
Public-domain text, read in full here on John Shaqi.
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