Which archimedean solids can't be generated with triangle tilings?
Polyhedra are generated by reflecting a
across each of its edges, over and over until a closed
polyhedron is made.
Since all of the angles of the generating triangle
(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.