Why can't you form a sixth Platonic solid by identifying faces of tetrahedrons?

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[SOLVED] platonic solids

Homework Statement



Let f_1 be a face of one tetrahedron and let f_2 be a face on a second same-sized tetrahedron. Why do you not get a sixth Platonic solid when you identify f_1 and f_2, which you can do because they are the same triangle?

Homework Equations


The Attempt at a Solution

 
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For a platonic solid, the same number of faces have to meet at each vertex.