I made a copy of a classic Soviet Constructivist-style poster, largely to understand this form better. I began by laying out guides, intially think to do it in a diamond pattern (square at 45 degress), but then deciding on mostly straight vertical and some horizontal guides, intersecting at key points of interest where multiple forms collided. I kept them in the same layer as the original image.
Where colour was needing to be applied to complex "sub-shapes", I experimented using the Live Paint Bucket tool. It was surprisingly effective, rather than duplicating shapes and recombining them in Pathfinder etc. I used the swatch set predefined for Russian poster art in Illustrator. I also set a rectangle filled with an off-white cream, as a pure white bg was too stark and left the objects feeling separated.
Font used is Agency FB 42pt Bold