Seven Triples puzzle

There are seven kinds of shape. There are three copies of each shape. The pieces like to group together in threes.

Can you arrange the pieces into seven groups of three so that for *each possible pair* of shapes, there is *one group* containing that pair?

Try to do it without paying attention to colours first, then try to rearrange the pieces so each group has a piece of each colour in it.

There's some nice maths behind why this puzzle works.

These pieces were designed using Blender 2.8. Print three copies of each piece, in different colours.