 The key construction at the heart of our framework is a novel Euler transformation that we introduced recently in a separate manuscript. 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.
<clarity>  The key construction at the heart of our framework is a novel Euler transformation that we introduced recently in a separate manuscript. 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.
 The key construction at the heart of our framework is an Euler transformation which 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.