how to draw a unit length cube with diagonal passing through (0,0,0) and (2,2,2)

Question

I am confused on the passing through (0,0,0) and (2,2,2) part;

it is not said that the cube lies at origin.

So how we determine all the points of cube?

Answer 1

Any unit square with it’s bottom left corner located on the line x=y=z will have it’s diagonal passing through both (0,0,0) and (2,2,2) assuming the diagonal is taken from the bottom front left corner to the back top right corner. The points of all the cubes satisfying this are:

Bottom face {P1=(x,x,x),P2=(x+1,x,x),P3=(x,x+1,x),P4=(x+1,x+1,x)}

Top face {P5=(x,x,x+1),P6=(x+1,x,x+1), P7=(x,x+1,x+1), P8=(x+1,x+1,x+1)}