Here's my first attempt at the 30 squares model. I needed to be a little bit more careful in the measuring and cutting as not everything matches up - but it is still a really pleasing shape.

I realised that this shape is basically 5 intersecting cubes. Below is a simple cadboard model of 5 intersecting cubes:

You can see that the shapes are exactly the same- I have aligned the blue, yellow and red edges in both pictures