Geodesic
Non-extendible finite polycycles
Izvestiya. Mathematics , Tome 70 (2006) no. 1, pp. 1-18.

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We give a fairly simple proof of a result announced in [2] that there are only seven non-extendible finite $(r,q)$-polycycles: the tetrahedron without a face, the cube without a face, the octahedron without a face, the dodecahedron without a face, the icosahedron without a face, the split-vertex octahedron and the split-vertex icosahedron. 
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M. Deza; S. V. Shpektorov; M. I. Shtogrin. Non-extendible finite polycycles. Izvestiya. Mathematics , Tome 70 (2006) no. 1, pp. 1-18. http://geodesic.mathdoc.fr/item/IM2_2006_70_1_a0/

[1] Kharari F., Teoriya grafov, Mir, M., 1973 | MR | MR

[2] Deza M., Shtogrin M. I., “Ekstremalnye i nerasshiryaemye politsikly”, Tr. MIAN, 239, 2002, 127–145 | MR | Zbl

[3] Deza M., Shtogrin M., “Clusters of cycles”, J. of Geometry and Physics, 40 (2002), 302–319 | DOI | MR | Zbl

[4] Deza M., Shtogrin M. I., “Metrika postoyannoi krivizny na politsiklakh”, Matem. zametki, 78:2 (2005), 223–233 | MR | Zbl

[5] Zeifert G., Trelfall V., Topologiya, NITs “Regulyarnaya i khaoticheskaya dinamika”, Izhevsk, 2001

[6] Novikov S. P., Topologiya, IKI, Moskva–Izhevsk, 2002