I recommend you get some thin cardboard or stiff paper. The idea is to make the two halves resulting from cutting a cube along a plane through its center, and orthogonal to a major diagonal.
Pick a unit of measurement. Draw three squares, each two units on a side. For each, mark the midpoints of two consecutive edges. Draw the line segment between the two edges. Now you have three squares, each of which has a corner triangle. Cut out the squares, then further cut off the triangle corner pieces, Now you have three right triangles, edges $(1,1,\sqrt2),$ and three pentagons, edges $(2,2,1,\sqrt2,1).$ Finally, draw one regular hexagon, all edges $\sqrt 2.$ Cut that out as well.
Tape together the pentagons at their right angles, so you have part of a cube. Tape in the right triangles in the remaining three corners that have right angles. Finally, tape the hexagon where it fits.
Make another one.
Place them with the hexagons matching up, see what happens.
Oh, well, pictures at http://mathworld.wolfram.com/Cube.html . I still recommend you construct these yourself.