  In our earlier papers we constructed examples of 2-dimensional nonaspherical
simply-connected cell-like Peano continua, called {\sl Snake space}. In the
sequel we introduced the functor $SC(-,-)$ defined on the category of all
spaces with base points and continuous mappings. For the circle $S^1$, the
space $SC(S^1, \ast)$ is a Snake space. In the present paper we study the
higher-dimensional homology and homotopy properties of the spaces $SC(Z, \ast)$
for any path-connected compact spaces $Z$.
