a 3D paper sculpture with a tessellation of kangaroos
from well-known tessellation artist Bruce Bilney of Australia

Bruce Bilney's tessellation tetrahedron of kangaroos

There are a few 3D shapes that can be made by assembling "regular polygons"-- that is, you can make some solid stuff by putting together equilateral triangles, squares, and hexagons. These 3D shapes are what geometry teachers call "Platonic Solids".

The piece at left is a "Tetrahedron", which is a pyramid shape made from triangles, and for which all the sides and edges are the same size.

Before you print out and assemble the design Bruce has made, can you guess whether the kangaroos will meet up perfectly along every edge? ...Or will there be an edge or two where kangaroos are being senselessly cut into unhappy half-kangaroos and wild things with two heads or two tails?

You can see much more of Bruce Bilney's tessellation art at his website, Ozzigami.com.au