Geodesic
On Polyhedral Realizability of Certain Sequences
Canadian mathematical bulletin, Tome 12 (1969) no. 1, pp. 31-39

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A finite sequence (pk) = (p3, p4,...) of non-negative integers shall be called realizable provided there exists a 3-valent 3-polytope P which has pi. i-gonal faces for every i. P is called a realization of (pk).For realizability of a sequence (pk), from Euler's formula follows (*) as a necessary condition. 
Jucovič, E. On Polyhedral Realizability of Certain Sequences. Canadian mathematical bulletin, Tome 12 (1969) no. 1, pp. 31-39. doi: 10.4153/CMB-1969-004-1
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     author = {Jucovi\v{c}, E.},
     title = {On {Polyhedral} {Realizability} of {Certain} {Sequences}},
     journal = {Canadian mathematical bulletin},
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     year = {1969},
     volume = {12},
     number = {1},
     doi = {10.4153/CMB-1969-004-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-004-1/}
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