Three more geometrical puzzles. Don’t you like polyhedra? These are the last two geometrical questions. Then, I will have for you numerical ones.

1.09 Four regular tetrahedrons are placed inside a regular tetrahedron that has edges of double length. This is done in such a way that each vertex of the large tetrahedron coincides with one of the vertices of the small tetrahedrons, so that an empty space is left in the middle of the large tetrahedron. Please describe in words the shape of the empty space.

1.10 Two ants are on the opposite vertices of a regular octahedron. They choose at random one of the edges and walk on it at the same uniform speed. Every time each of the ants encounters a vertex, it immediately chooses at random a new edge (that is, it never doubles back onto the edge it has just come from) and walks on it. What is the probability that the two ants meet after each ant has walked on exactly two edges?

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