A sphere represents finite boundariless surface with constant positive curvature, while a Clifford's torus represents finite boundariless surface with constant zero curvature.
Both of these surfaces have neither edges nor vertices.
Meanwhile, tractricoids, a kind of pseudosphere, represents finite surface with constant negative curvature, but it has ‘sharp’ edges and vertex, along the equator and poles respectively.
Is there a pseudosphere that is both finite and boundariless, and having neither edges nor vertices (like a sphere or Clifford's torus, unlike a tractricoid)?