  Linear constraints for a matrix polytope with no fractional vertex are
investigated as intersecting research among permutation codes, rank
modulations, and linear programming methods. By focusing the discussion to the
block structure of matrices, new classes of such polytopes are obtained from
known small polytopes. This concept, called "consolidation", is applied to find
a new compact graph which is known as an approach for the graph isomorphism
problem. Encoding and decoding algorithms for our new permutation codes are
obtained from existing algorithms for small polytopes. The minimum distances
associated with Kendall-tau distance and the minimum Euclidean distance of a
code obtained by changing the basis of a permutation code may be larger than
the original one.
