Which archimedean solids can't be generated with triangle tilings?

Polyhedra are generated by reflecting a
triangle
across each of its edges, over and over until a closed
polyhedron is made.
Since all of the angles of the generating triangle
are nice
(are 180/n degrees for some whole number n), the number of times
the triangle is repeated around each vertex is always an even
(360/[180/n] = 2n times).

That means that each edge of the generating triangle is a part of a line that
goes around the entire generated polyhedron, dividing it
into two symmetrical parts. The plane dividing the two
halves is called the plane of symmetry.

Since the
snub cube
and the
snub dodecahedron
have no planes of symmetry, they cannot be generated this way.