Multidimensional triangle-truncated simplexes

We consider the convex polytopes, called triangle-truncated simplexes. From the point of view of a constructive object in four and higher dimensions vector space such polytopes are multidimensional analogs of one classical semi-regular polytopes, namely, truncated tetrahedron.
We present results of investigations of inner geometrical structure and combinatorial characteristics of the complete assemblage of faces of triangle-truncated simplexes in vector spaces of arbitrary dimension. We formulate and prove a theorem about the volumes of multidimensional truncated simplex of generalized kind in Euclidean space.