Constructing a Platonic solid

Geometry Level 5

You have a collection Platonic solids each having an edge length of one, You realize that you can glue them all together to construct a much larger Platonic solid, which may or may not be one of the types you already have (leaving no gaps or holes).

If you have exactly 364 of one of the solids, how many solids do you have altogether?

Inspiration: Michael Mendrin

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