Are there molecules that take the shape of every platonic solid?
Yes, for each of the 5 platonic solids, there is at least one molecule that takes its shape.

There exist tetrahedron-shaped molecules. Some instances are $\text{CH}_4$ or $\text{CCl}_4$.

There exist octahedron-shaped molecules. Some instances are $\text{SF}_6$ or $\text{Mo(CO)}_6$.

There exist hexahedron-shaped molecules. An instance would be $\text{C}_8\text{H}_8$ AKA "cubane". Perhaps simple cubic lattices (like NaCl) could be considered "hexahedral molecules" as well?

There exist icosahedron-shaped molecules. An instance is elemental boron, $\text{B}_{12}$.

There exist dodecahedron-shaped molecules. An instance is dodecahedrane ($\text{C}_{20}\text{H}_{20}$).