Hexagons
Why a hexagonal weave? Suppose you are making a basket. You make a circular rim (black). Then you wrap your strands (grey) around the rim so that they are as close as possible without crossing. As long as the rim is the same width as the strands, this will always make a 60 degree angle! No wonder the technique is found in so many Indigenous cultures.
If the weave is flat, then it is simply a hexagonal lattice.This is much like the structure of graphite.
Graphite: stacks of hexagonal layers (which is why it is slippery; the layers can slide).
A hexagonal basket weave in a Baka village in Cameroon:
Pentagons
When they want to make a corner, the weavers introduce a pentagonal hole
A few pentagonal holes make corners for this flat bottom (Mozambique)
This Malaysian ball is nothing but corners!