A2 From each of the eight vertices of a cube, a piece is sawn off so that instead of a vertex, a triangular face with three vertices appears. Each pair of the 24 vertices of the resulting body is connected by a line segment.

How many of these line segments lie, except for their endpoints, entirely within the body?

![](https://cdn.mathpix.com/cropped/2024_04_17_3181bece6cd13f041828g-1.jpg?height=294&width=279&top_left_y=1646&top_left_x=1531)
A2 The corner A2 is connected to the 23 other corners. Among these line segments, there are always 3 edges and $2 * 5$ face diagonals, see figure. Therefore, from each corner, there are 10 line segments that lie within the cube. From the 24 corners, this results in $24 * 10$, but each line segment is counted twice. In total, therefore, 120.

![](https://cdn.mathpix.com/cropped/2024_04_17_6b845a2526b379866c18g-1.jpg?height=308&width=294&top_left_y=620&top_left_x=1532)