  Axial algebras of Jordan type $\eta$ are a special type of commutative
non-associative algebras. They are generated by idempotents whose adjoint
operators have the minimal polynomial dividing $(x-1)x(x-\eta)$, where $\eta$
is a fixed value that is not equal to $0$ or $1$. These algebras have
restrictive multiplication rules that generalize the Peirce decomposition for
idempotents in Jordan algebras. A universal $3$-generated algebra of Jordan
type $\frac{1}{2}$ as an algebra with $4$ parameters was constructed by I.
Gorshkov and A. Staroletov. Depending on the value of the parameter, the
universal algebra may contain a non-trivial form radical. In this paper, we
describe all semisimple $3$-generated algebras of Jordan type $\frac{1}{2}$
over a quadratically closed field.
