GeoGebra also comes with a powerful 3-D panel, where Liu Hui's Cube Puzzle can be modeled on the basis of a cube by constructing three face diagonals (*FH*, *BD*, *BE*) and one internal diagonal (*BH*) as shown in **Figure 17**. To define the three solids in Liu Hui's dissection, one can use the *prism tool* for the *qiandu* (green triangular prism) piece and the *pyramid tool* for the *yangma* (red rectangular pyramid) and the *bie'nao* (purple triangular pyramid). By rotating the 3-D view, one can obtain a better picture of all three solids. GeoGebra further has a *net* tool that flattens a chosen polyhedron to a template on a plane. Modeling Liu Hui's Cube Puzzle in GeoGebra 3-D allows students to appreciate the relationships between 3-D geometric operations and 2-D templates and further develop increasingly complex spatial reasoning skills, which are strikingly lacking in traditional school mathematics.

**Figure 17a**. Liu Hui's Cube Puzzle can be modeled using construction tools in the 3-D panel of GeoGebra. Click then drag the image above to see the dissection from different perspectives.

**Figure 17b**. Use the slider to fold up the 2-D nets into the 3-D pieces of Liu Hui's Cube Puzzle; namely, a red *qiandu,* green *yangma,* and blue *bie'nao *(GeoGebra applet by Lee Stemkoski).

**Figure 17c**. Use the slider to "solve" Liu Hui's Cube Puzzle; that is, to fit the red *qiandu,* green *yangma,* and blue *bie'nao *together to form a cube. You may also move the three pieces into position by dragging them* *(GeoGebra applet by Lee Stemkoski).