  Carbon is the most important chemical element and the theoretical study of
its new allotropes can be of great interest. In this study, regular
dodecahedron (dodecahedrane) oligomers (n = 1, 3, 5, 7, 9, 11, 13) by extending
the dodecahedrane units in 3-dimensions were designed. Then, a theoretical
study was conducted on their structures and electronic properties as potential
new carbon allotrope. The cohesive energy (Ecoh) and $\Delta$G, were
calculated. Experimental observations indicate that the Ecoh rises as the
number of dodecahedrane units increases, whereas the Gibbs free energy change
$\Delta$G decreases with an increase in the number of dodecahedrane units. The
HOMO-LUMO energy gap (Eg) values, which represent electronic properties,
decrease with increasing number of dodecahedrane units. Density functional
theory (DFT) calculations of the novel carbon allotropes polydodecahedrane
nanostructures have unveiled a previously unobserved symmetry, indicating
intrinsic metallic behavior. The symmetrical distribution of partial charges
was found in molecular electrostatic potential (MEP) diagrams for all
oligomers, showing a tendency of the structures to maintain a symmetrical
structural order as the number of monomer units increases. In addition, natural
bond orbital (NBO) analysis of 13-units oligomer as largest designed structure
reveals near-$sp^3$ hybridization for different carbons. Based on the
calculated results, the structures have a tendency to extend in 3-dimensions
and form a covalent network of poly-dodecahedrane with a unique structure
consisting of interconnected cyclopentane rings. The results show that this
exclusive configuration exhibits theoretical stability and suggests the
potential for poly-dodecahedrane to be regarded as a novel carbon allotrope.
