Ah no, Emilio, a lectotype is a specimen that is selected (and published)
as the holotype from a series of syntypes. Until such a selection is
published, all the syntypes are of equal rank, which can cause difficulties
if they prove to belong to more than one species, as has frequently
happened. "Lectotype" is a fully acceptable modern term, unlike "cotype".
Incidentally, lectotypes (and neotypes, which replace lost or destroyed
holotypes) should be proposed only during the revision of a species, genus,
or family, not as a matter of curatorial tidiness. Picking the wrong
lectotype can cause more harm than good.

You have, however, correctly described an earlier concept of the "type
specimen" itself. Some workers, such as T. A. Conrad, would make a
composite drawing of a new species, based on several specimens (none of
which might be complete). The drawing thus represents no single specimen,
but a reconstruction or ideal concept of a species. In most cases, Conrad
did it well; nevertheless, it is disconcerting when one finds that none of
the syntypes match the drawing.

Andrew K. Rindsberg
Geological Survey of Alabama

"I hope we stay serene and calm
When Alabama gets the Bomb."
        Tom Lehrer, "Who's Next?"