  The superstring and superbrane theories which include gravity as a necessary
and fundamental part renew an interest to alternative representations of
general relativity as well as the alternative models of gravity. We study the
coframe teleparallel theory of gravity with a most general quadratic
Lagrangian. The coframe field on a differentiable manifold is a basic dynamical
variable. A metric tensor as well as a metric compatible connection is
generated by a coframe in a unique manner. The Lagrangian is a general linear
combination of Weitzenb\"{o}ck's quadratic invariants with free dimensionless
parameters $\r_1,\r_2,\r_3$.
  Every independent term of the Lagrangian is a global SO(1,3)-invariant
4-form. For a special choice of parameters which confirms with the local
SO(1,3) invariance this theory gives an alternative description of Einsteinian
gravity - teleparallel equivalent of GR.
  We prove that the sign of the scalar curvature of a metric generated by a
static spherical-symmetric solution depends only on a relation between the free
parameters. The scalar curvature vanishes only for a subclass of models with
$\r_1=0$. This subclass includes the teleparallel equivalent of GR. We obtain
the explicit form of all spherically symmetric static solutions of the
``diagonal'' type to the field equations for an arbitrary choice of free
parameters. We prove that the unique asymptotic-flat solution with Newtonian
limit is the Schwarzschild solution that holds for a subclass of teleparallel
models with $\r_1=0$. Thus the Yang-Mills-type term of the general quadratic
coframe Lagrangian should be rejected.
