  The discrete cosine transforms of types V--VIII are generalized to the
antisymmetric and symmetric multivariate discrete cosine transforms. Four
families of discretely and continuously orthogonal Chebyshev-like polynomials
corresponding to the antisymmetric and symmetric generalizations of cosine
functions are introduced. Each family forms an orthogonal basis of the space of
all polynomials with respect to some weighted integral. Cubature formulas,
which correspond to these families of polynomials and which stem from the
developed discrete cosine transforms, are derived. Examples of
three-dimensional interpolation formulas and three-dimensional explicit forms
of the polynomials are presented.
