Three-sided shapes will tessellate.
Last year I blogged about tessellating designs for quilts---pattern that fills the surface with just one shape.
Six-sided shapes will tessellate
Just in case you wake up one morning and say: One Piece. That will simplify my life!
I started the series on this Material Culture blog.
3-SIDED SHAPES TRIANGLES
Irregular 4-sided Shapes
Carol Gilham Jones: Sixty Degrees of Tessellation
Mennonite Quilt from Stella Rubin's shop - 5 sided shape
8-sided shapes won't tessellate
7 & 8 SIDED SHAPES WON'T WORK
Hexagons have the most variations.
I did many posts on patterns with regular and irregular six-sided shapes.
6-SIDED SHAPES HEXAGONS
So many that I had to start a new blog because the pattern indexing was taking over the old blog.
The rest of these are on the CloudofQuiltPatterns blog.