Liu Hui was a 3rd century Chinese mathematician, perhaps best known for a dissection proof of the Pythagorean Theorem (Shang Gao Theorem (商高定理)). Recently I’ve been exploring the trisection of a cube, so students could discover the formula for the volume of a pyramid or cone. After recreating the correct pyramids myself – which took an embarrassingly long time and involved floral foam, lucite boxes, ribbon, and my Dremel tool, but I did it – I came upon this image, which amazed me.

 I was so excited that I made and built these nets for Liu Hui’s solids.

What is so amazing about these is their relationship to the cube and to each other.

Bienao is one-sixth of a cube.

Yangma is one-third of the cube.

Qiandu is one-half of the cube.

Bienao is one-third of Qiandu.

Bienao is one -half of Yangma.

Yangma is two-thirds of Qiandu.

Qiandu, Yangma, and Bienao together make a cube.

Wow.

I bought printed card stock and tiny, strong magnets and started building them. (Resources)

   

 

Next, rhombic dodecahedra.