Type II structure is cubic. In addition to pentagonal dodecahedra, hydrocarbons are also enclosed by polyhedra with 4 hexagonal and 12 pentagonal faces (of course somewhat distorted. The polyhedron has tetrahedral symmetry and is shown below in a number of orientations.
Clusters of these solids link tetrahedrally by sharing faces.
The voids between three 16-faced solids are filled by triads of dodecahedra (of course, to join this way, the dodecahedra must also be slightly distorted, since the dihedral angle of a true pentagonal dodecahedron is only 116.5 degrees, not 120 degrees)
The result is that tetrahedral clusters of 16-faced polyhedra (below, left) are surrounded by cages of dodecahedra (below right).
Below are views of a cluster of 16-faced polyhedra and a cluster with enclosing dodecahedra, viewed along a 4-fold inversion axis.
Below is part of the lattice, viewed along a 4-fold inversion axis. The network of 16-faced polyhedra is shown on the left, and the network with interstitial dodecahedra is shown on the right.
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