Archimedean graph designs

Forbes, A. D. and Griggs, T. S. (2013). Archimedean graph designs. Discrete Mathematics, 313(11) pp. 1138–1149.

DOI: https://doi.org/10.1016/j.disc.2011.11.012

Abstract

We prove that the complete graph Kv can be decomposed into truncated cuboctahedra if v ≡ 1 (mod 144), into icosidodecahedra if v ≡ 1 (mod 120), into rhombicosidodecahedra if v ≡ 1 (mod 240), into truncated icosahedra if v ≡ 1 (mod 180), into truncated dodecahedra if v ≡ 1 (mod 180), into truncated icosidodecahedra if v ≡ 1 (mod 360), into snub cubes if v ≡ 1 (mod 120), and into pseudo-rhombicuboctahedra if and only if v ≡ 1 or 33 (mod 96).

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