Amanda from Wallace Hall Academy has sent us a solution to the first part of the question:
You make a regular octagon by making the outline of it with triangles. To do this, you make one quarter of the pattern (i.e. a quarter of the whole interactivity image) orange, so there is an orange square. Then you make the smaller triangles on the edges purple. Then you make the central octagon white, and you will have an octagon outlined by orange big triangles and purple small triangles.
Here is a picture of Amanda's octagon and triangles, using just one quarter of the pattern:
Ling from Beecroft Primary School, Australia has found a way of producing irregular hexagons with triangles and squares. Here is the image she sent: