Repeating textures requires redundant vertices?

If I wanted to repeat a texture along a long, narrow polygon, do I have to add redundant vertices along the polygon to allow for specifying the texture coordinates? Is it possible to specify a texture coordinate w/o specifying a vertex?

If this is the case, is it considered better to add the redundant vertices or to extend the original texture into a larger one that simply repeats. I assume that extra vertices is the way to go, but any thoughts would be welcome.

Thanks in advance,

von

Say you had a rectangular quad and you wanted texture to repeat 16 times along length, you should be able to specify the tex coords as (0, 0) and (1, 0) at one end and (0,16) and (1,16) at the other end or something like that. And then make sure to specify GL_REPEAT as the texenv mode.