How to create multiple shapes with specified diagonal space alignment

Hi

I am trying to make such a design

what is the best way to do this ensuring i have total control over the width of the space between. so if i want 1 mm between each shape across the board, i can do that. right now i am doing some trial and error but i can't seem to make the diagonals perfectly aligned. i don't want to draw lines i want it to be done through spacing only. how would i go about doing this.