1. The first problem describes a right rectangular parallelepiped with height 6 units and vertex $D_1(4,5,0)$. We need to find the coordinates of the other vertices. 2. Since $D_1$ lies on the base plane (z=0), and the height is 6, the top vertices will have z-coordinate 6. 3. The parallelepiped has edges $AA_1$, $BO$, $CC_1$, $DD_1$ as lateral edges, so the base vertices are $A, B, C, D$ with $A_1, B_1, C_1, D_1$ on the base plane. 4. Given $D_1(4,5,0)$, and height 6, the top vertex $D$ is at $(4,5,6)$. 5. Since $O$ is the origin $(0,0,0)$, and $B$ lies on the x-axis or y-axis, we can deduce the coordinates of $A, B, C$ by the rectangular shape and edges. 6. The base is a rectangle with vertices $A_1, O, C_1, D_1$; $O$ is at $(0,0,0)$, $D_1$ at $(4,5,0)$, so $A_1$ and $C_1$ are at $(0,5,0)$ and $(4,0,0)$ respectively. 7. The top vertices $A, B, C, D$ are obtained by adding height 6 to the z-coordinate of the base vertices $A_1, O, C_1, D_1$: $$A = (0,5,6), B = (0,0,6), C = (4,0,6), D = (4,5,6)$$ Final coordinates: $A(0,5,6), B(0,0,6), C(4,0,6), D(4,5,6), A_1(0,5,0), O(0,0,0), C_1(4,0,0), D_1(4,5,0)$