Draw a circle using the compass, and mark the center point. Use your straightedge to draw a horizontal line passing through the center of this circle, and extend that line left and right so that the parts of the line lying outside of the circle are equal to the radius of the circle. Place the needle of your compass on the endpoints of these lines, and draw two more circles identical with the first one.
Construct two lines perpendicular to the line joining the center of the three circles. These two lines should pass through the points where the circumference of the center circle touches the circumferences of the other circles. Make sure that these two lines are approximately three times that of the diameter of your three circles.
Set your compass to draw a circle having the same diameter of the original circles. Place the needle of the compass on the vertical line on the left, such that the pencil lies on the circumference of the center circle. Draw a new circle here, whose circumference touches the circumference of the two circles below it.
Repeat the process for the part of the leftmost line that lies below the two leftmost circles, and for the upper and lower parts of the right-hand line. The end result should be seven circles, with one in the center and six more arranged around it, with each one of the outer six being equidistant from the center of the first circle.
Use your straightedge to connect the center of each circle with the centers of every circle touching it. Erase the circles, or make the lines bold, and the lattice of alternating tetrahedrons and octahedrons is the isotropic vector matrix. To expand the matrix to 3-dimensions, just replace the circles with spheres.