(Some contributions by Advanced Shmuzzlers are here.)
The technical term for a shape which can be Shmuzzled is "Tessellation Shape." Most things are not Tessellation shapes because no matter how you put them together, there are spaces left in between.
Here are some shapes which cannot be Shmuzzled:
Here are some common Tessellation Shapes:
The simplest Tessellation Shapes are Polygons.
All Triangles are Tessellation Shapes.
All Quadrilaterals are Tessellation Shapes.
Some Pentagons are Tessellation Shapes.
NOTE: Regular pentagons are not Tessellation Shapes.
Some Hexagons are Tessellation Shapes.
Create Shmuzzling Creatures of your own by modifying polygons. For example:
Parallelograms
Triangles
(Also try starting with squares, rectangles, hexagons and other figures.)
Contributions by Advanced Shmuzzlers:
Conshmuzzion Worker
Dale, Urbana IL
Fit 'em Fin
Eve, Naperville IL
John Shmuvolta
Roger, Sunnyvale CA
Click here for Teacher's Resources on Tessellation