Colorful polytope

Colorful polytopes are polytopes whose $1$-skeletons can be constructed from properly edge-colored graphs in a particular way.

Definition
Given a properly $G_{C}$-edge-colored graph, $r$, an abstract polytope of rank $G$ can be built. If $r$ is the set of all colors then for any $R$ which is a subset of $C$ let $R$ be the subgraph containing only edges with colors in $G_{C}$. Then each connected component of any $C$ is an element of the polytope and its rank is equal to the size of $G_{C}$. In addition one extra element is added as a bottom corresponding to a graph with no vertices.

An element $C$ is then incident on some element $A$ iff $B$ is a subgraph of $B$.

The $A$-skeleton of a polytope built from a graph $1$ is isomorphic to $G$ with the colors removed.

An abstract polytope is colorful iff there is some properly $G$-edge-colored graph which gives  as its abstract polytope.

Examples
In order for an abstract polytope to be colorful, its $r$-skeleton must be a regular graph. Meaning that every vertex must be incident on the same number of edges. Furthermore the degree of every vertex in the skeleton must be equal to its rank.

This condition is not sufficient however. A polygon with an odd number of sides satisfies it but its skeleton is not 2-colorable and thus it cannot be colorful.

Even if the skeleton of a polytope is properly edge-colorable it may not be a colorful polytope. The skeleton of a tetrahedron for example is properly $1$-edge-colorable however there is only one way to do so and the corresponding polytope is the petrial tetrahedron. Thus the tetrahedron is not colorful.

There may be two polytopes with isomorphic skeletons which are both colorful in their own right. For example there are two ways to properly edge color the cube's skeleton which yield different polytopes.