[ Skeletons of Polyhedral Figures ]

A toy factory produces wireframe cubes, with small colorful beads located at their vertices. According to the GOST standard, each cube must use beads of all eight colors (white and the seven colors of the rainbow). How many different models of cubes can the factory produce?

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If a cube is fixed, then 8 different balls can be placed at its vertices in 8! ways. But the cube can be rotated: each of its six faces can be made the bottom one and placed on it in four ways. Therefore, each cube corresponds to $6 \cdot 4=24$ "colorings", and the total number of models is $8! / 24=8 \cdot 7 \cdot 6 \cdot 5=$ 1680.

## Answer

1680 models.