Irregular meshgrid - how to create?

I wish to create an irregular meshgrid to simulate the positions of an atomic lattice plane.

The plane is body-centred-cubic.

The unit of the plane is a rectangle of dimensions x,y:

sqrt2 x 1

Atom sit at the corners of the rectangle, and one the centre. I want the mesh to have co-originates where the atoms sit

So, if I had the origin at the bottom left of the unit rectangle, there would be co-ordinate positions (x,y)

0,0 (bottom left of rectangle) sqrt(2),0 (bottom right of rectangle)

1/2sqrt(2) , 1/2 (centre of the rectangle)

0,1 (top left rectangle) sqrt(2) , 1 (top right rectangle)

Then the rectangles need to be tiled into a large mesh, maybe 25 atoms high.

kind regards W