The place where two faces (planes) intersect is called an edge.
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It is a vertex.
the place where two faces intersect
Two lines cross or intersect at a point.
No. The faces of a tetrahedron are equilateral triangles, but none of the faces is parallel to another one of the faces -- they could not be parallel, since by the definition of a tetrahedron, all the faces intersect(!) and parallel planes do not intersect.
A vertex.