 Our Euler transformation converts a 2-dimensional cell complex K into a new 2-complex K^ such that every vertex in the 1-skeleton G^ of K^ has degree 4.
<meaning-changed>  Our Euler transformation converts a 2-dimensional cell complex K into a new 2-complex K^ such that every vertex in the 1-skeleton G^ of K^ has degree 4.
 Our Euler transformation converts a 2-dimensional cell complex K into a new 2-complex K^ such that every vertex in the 1-skeleton G^ of K^ has even degree.