## Task 3 - 180933

Given is a cube, whose volume is denoted by $V_{1}$.

If the center of each face of this cube is connected to the centers of all adjacent faces, the edges of a regular octahedron are obtained. The volume of this octahedron is called $V_{2}$.

If the centroid of each face of this octahedron is now connected to the centroids of all adjacent faces, the edges of a second cube are obtained. Its volume is called $V_{3}$.

Calculate the ratio $V_{1}: V_{2}: V_{3}$!