When using the array form of operator new[](), the pointer returned points to the first element of the array. When creating multidimensional arrays with new, all array sizes must be supplied (although the leftmost dimension doesn't have to be a compile-time constant):

mat_ptr = new int[3][10][12];    // OK
mat_ptr = new int[n][10][12];    // OK
mat_ptr = new int[3][][12];      // illegal
mat_ptr = new int[][10][12];     // illegal

Although the first array dimension can be a variable, all following dimensions must be constants.