# Constructing a Platonic solid

**Geometry**Level 5

You have a collection of Platonic solids each having an edge length of one, Lets call these "unit Platonic solids". You realize that you can glue them all together to construct a much larger Platonic solid leaving no gaps or holes.

In your final construction (one large Platonic solid) you have used exactly 364 of one type of the unit Platonic solids, but may have used other types of unit Platonic solids as well.

How many unit Platonic solids did you use altogether in this final construction?

For example, if your final consturction is a Platonic solid mad up of 364 unit cubes and 212 unit tetrahedra, then your final answer would be 576.

**Inspiration:** Michael Mendrin