34. Unfolding a Cube. Models of polyhedra are made from flat nets. In a net, faces are adjacent to each other along edges, and the model is constructed by folding the cardboard net along the edges. A regular tetrahedron has two such different nets. How many does a cube have?
34. All existing nets (a total of 11) are shown in Fig. 49. The first six solutions give nets in which four faces of the cube are arranged in one strip of the net. No other solutions of this type exist. The next four nets are those in which there are three faces in one

![](https://cdn.mathpix.com/cropped/2024_05_21_5d77f4829f88503a49eag-086.jpg?height=817&width=834&top_left_y=437&top_left_x=611)

Fig. 48.
![](https://cdn.mathpix.com/cropped/2024_05_21_5d77f4829f88503a49eag-086.jpg?height=922&width=1186&top_left_y=1388&top_left_x=434)

Fig. 49.

strip, but not four faces. Finally, in the last net, there are no three faces in any strip.