
The tesseract is a four dimensional cube. It has 16 edge points
v=(a,b,c,d), with a,b,c,d either equal to +1 or 1. Two points are connected,
if their distance is 2. Given a projection
P(x,y,z,w)=(x,y,z) from four dimensional space to three dimensional space,
we can visualize the cube as an object in familar space.
The effect of a linear transformation like a rotation
 1 0 0 0 
R(t) =  0 1 0 0 
 0 0 cos(t) sin(t) 
 0 0 sin(t) cos(t) 

in 4d space can be visualized in 3D by viewing
the points v(t) = P R(t) v in R_{3.
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