Geodesic
A Generation Procedure for the Simple 3-Polytopes With Cyclically 5-Connected Graphs
Canadian journal of mathematics, Tome 26 (1974) no. 3, pp. 686-708

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In this paper we derive a generation procedure for the simple (3-valent) 3-polytopes with cyclically 5-connected graphs. (A graph is called cyclically n-connected if it cannot be broken into two components, each containing a cycle, by the removal of fewer than n edges.) We define three new types of face splitting and we show, in Theorems 16 and 17, that the simple 3-polytopes with cyclically 5-connected graphs are exactly the polytopes obtained from the dodecahedron by these face splittings. 
Butler, Jean W. A Generation Procedure for the Simple 3-Polytopes With Cyclically 5-Connected Graphs. Canadian journal of mathematics, Tome 26 (1974) no. 3, pp. 686-708. doi: 10.4153/CJM-1974-065-6
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