facets

a set of growing shapes made up with squares and equilateral triangles

[a dodecagon after step 2]

with number patterns that aren't too easy to discern
but are regular

what will the next two shapes look like, for n = 5 and for n = 6?

for n = 5,

• why will there be 26 extra triangles?
• why will there be 14 extra squares?

a block (side) of n squares goes to 2n + 1 triangles in the next ring

m triangles goes to? squares in the next ring?

it might also be helpful to focus on the shapes that surround an 'interior' point

a ppt is here