  Assume that $G$ is a homeomorphically peripheral color alternating graph with
inner dual $G^*$ and resonance graph $R(G)$. We first establish a bijection
between the set of maximal hypercubes of the resonance graph $R(G)$ and the set
of maximal independent sets of the inner dual $G^*$, where $G^*$ is a tree and
isomorphic to the $\tau$-graph of $R(G)$. A novel characterization on when
resonance graphs are daisy cubes follows naturally. Furthermore, the proof of
the characterization provides a binary code labelling for the vertex set of a
resonance graph $R(G)$ as a daisy cube with respect to the set of maximal
independent sets of the inner dual $G^*$ of $G$. We then show that a daisy cube
with at least one edge is a resonance graph of a plane bipartite graph if and
only if its $\tau$-graph is a forest. As applications of our main theorems,
interesting results are obtained for Fibonacci cubes and Lucas cubes which are
special types of daisy cubes. Structure properties are also provided for daisy
cubes whose $\tau$-graphs are trees and have at most five maximal hypercubes.
We conclude the paper with two algorithms which provide a binary code labelling
for the vertex set of a resonance graph as a daisy cube.
