Cavity pentagonal dodecahedron

The pentagonal dodecahedron (12-sided cavity) of Figure 2.5 is labeled 512 because it has 12 pentagonal faces ( i = 5, nti = 12) with equal edge lengths and... 

Figure 2.5 Three cavities in gas clathrate hydrates (a) pentagonal dodecahedron (512), (b) tetrakaidecahedron (51262), (c) hexakaidecahedron (51264), (d) irregular dodecahedron (435663), and (e) icosahedron (51268).

Pentagonal Dodecahedra. The basic building block, present as the small cavity in all known natural gas hydrate structures, is the 512 pentagonal dodecahedron of Figure 2.5a. When 12 pentagons are combined, the 512 structure results. All 60 of the molecules in the 12 pentagons are not required for the structure because pentagons share sides, only 20 molecules are required to make a 512 cavity. 

Figure 1 Different cavities found in gas hydrates (a) pentagonal dodecahedron (b) tetrakaidecahedron (c) hexakaidecahedron.

Fig. 10.2, they are pentagonal dodecahedron (5 " ), tetrakaidecahedron (5 6 ), hexakaidecahedron (5 6" ), irregular dodecahedron (4 5 6 ), and icosahedron (5 6 ). The formalism X" is used to describe the structure of each cavity, where X denotes the type of cage face (4—square, 5-pentagon, and 6-hexagon), and n represents the number of such kinds of face in that cavity. The three structures of gas hydrates comprise different cavities 5 and 5 6 cavities form si, 5 and 5 6 cavities form sll, and sH is formed by 5, 4 5 6, and 5 6 cavities. 

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