### Abstract

The complexity of 13 Archimedean solids via their Schlegel graphs was studied by four indices: the complexity index based on the augmented vertex-degree, and the total numbers of walks, trails and paths. All four descriptors consider the truncated tetrahedron, the truncated cube and the truncated octahedron as the least complex structures, and the rhombicuboctahedron, the icosidodecahedron, the rhombicosidodecahedron, the snub cuboctahedron and the snub icosidodecahedron the most complex structures among the 13 Archimedean solids. The ordering of remaining five Archimedean solids (the truncated icosahedron, the truncated dodecahedron, the cuboctahedron, the truncated cuboctahedron and the truncated icosidodecahedron) differs from index to index. The visualization of the complexity relationship between Archimedean solids is realized by the partial order of their indices in consonance with the Hasse diagram.

Original language | English (US) |
---|---|

Pages (from-to) | 119-132 |

Number of pages | 14 |

Journal | Journal of Mathematical Chemistry |

Volume | 39 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2006 |

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### All Science Journal Classification (ASJC) codes

- Chemistry(all)
- Applied Mathematics

### Cite this

*Journal of Mathematical Chemistry*,

*39*(1), 119-132. https://doi.org/10.1007/s10910-005-9008-2

}

*Journal of Mathematical Chemistry*, vol. 39, no. 1, pp. 119-132. https://doi.org/10.1007/s10910-005-9008-2

**On the complexity of Archimedean solids.** / Rajtmajer, Sarah Michele; Miličević, Ante; Trinajstić, Nenad; Randić, Milan; Vukičević, Damir.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the complexity of Archimedean solids

AU - Rajtmajer, Sarah Michele

AU - Miličević, Ante

AU - Trinajstić, Nenad

AU - Randić, Milan

AU - Vukičević, Damir

PY - 2006/1/1

Y1 - 2006/1/1

N2 - The complexity of 13 Archimedean solids via their Schlegel graphs was studied by four indices: the complexity index based on the augmented vertex-degree, and the total numbers of walks, trails and paths. All four descriptors consider the truncated tetrahedron, the truncated cube and the truncated octahedron as the least complex structures, and the rhombicuboctahedron, the icosidodecahedron, the rhombicosidodecahedron, the snub cuboctahedron and the snub icosidodecahedron the most complex structures among the 13 Archimedean solids. The ordering of remaining five Archimedean solids (the truncated icosahedron, the truncated dodecahedron, the cuboctahedron, the truncated cuboctahedron and the truncated icosidodecahedron) differs from index to index. The visualization of the complexity relationship between Archimedean solids is realized by the partial order of their indices in consonance with the Hasse diagram.

AB - The complexity of 13 Archimedean solids via their Schlegel graphs was studied by four indices: the complexity index based on the augmented vertex-degree, and the total numbers of walks, trails and paths. All four descriptors consider the truncated tetrahedron, the truncated cube and the truncated octahedron as the least complex structures, and the rhombicuboctahedron, the icosidodecahedron, the rhombicosidodecahedron, the snub cuboctahedron and the snub icosidodecahedron the most complex structures among the 13 Archimedean solids. The ordering of remaining five Archimedean solids (the truncated icosahedron, the truncated dodecahedron, the cuboctahedron, the truncated cuboctahedron and the truncated icosidodecahedron) differs from index to index. The visualization of the complexity relationship between Archimedean solids is realized by the partial order of their indices in consonance with the Hasse diagram.

UR - http://www.scopus.com/inward/record.url?scp=33644859613&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33644859613&partnerID=8YFLogxK

U2 - 10.1007/s10910-005-9008-2

DO - 10.1007/s10910-005-9008-2

M3 - Article

AN - SCOPUS:33644859613

VL - 39

SP - 119

EP - 132

JO - Journal of Mathematical Chemistry

JF - Journal of Mathematical Chemistry

SN - 0259-9791

IS - 1

ER -