The angle between the C-C bonds in each carbon atom is 108°, which is the angle between adjacent sides of a regular pentagon. That value is quite close to the 109.5° central angle of a regular tetrahedron—the ideal angle between the bonds on an atom that has sp hybridisation. As a result, there is minimal angle strain. However, the molecule has significant levels of torsional strain as a result of the eclipsed conformation along each edge of the structure.
The molecule has perfect icosahedral (I) symmetry, as evidenced by its proton NMR spectrum in which all hydrogen atoms appear at a single chemical shift of 3.38 ppm.  Unlike buckminsterfullerene, dodecahedrane has no delocalized electrons and hence has no aromaticity.