On the complexity of Archimedean solids

Sarah Michele Rajtmajer, Ante Miličević, Nenad Trinajstić, Milan Randić, Damir Vukičević

Research output: Contribution to journalArticle

6 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)119-132
Number of pages14
JournalJournal of Mathematical Chemistry
Volume39
Issue number1
DOIs
StatePublished - Jan 1 2006

Fingerprint

Archimedean solid
Icosidodecahedron
Cuboctahedron
Truncated dodecahedron
Complex Structure
Truncated icosidodecahedron
Rhombicosidodecahedron
Truncated cuboctahedron
Rhombicuboctahedron
Truncated cube
Truncated tetrahedron
Truncated octahedron
Vertex Degree
Partial Order
Visualization
Walk
Descriptors
Diagram
Path
Graph in graph theory

All Science Journal Classification (ASJC) codes

  • Chemistry(all)
  • Applied Mathematics

Cite this

Rajtmajer, S. M., Miličević, A., Trinajstić, N., Randić, M., & Vukičević, D. (2006). On the complexity of Archimedean solids. Journal of Mathematical Chemistry, 39(1), 119-132. https://doi.org/10.1007/s10910-005-9008-2
Rajtmajer, Sarah Michele ; Miličević, Ante ; Trinajstić, Nenad ; Randić, Milan ; Vukičević, Damir. / On the complexity of Archimedean solids. In: Journal of Mathematical Chemistry. 2006 ; Vol. 39, No. 1. pp. 119-132.
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Rajtmajer, SM, Miličević, A, Trinajstić, N, Randić, M & Vukičević, D 2006, 'On the complexity of Archimedean solids', 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.

In: Journal of Mathematical Chemistry, Vol. 39, No. 1, 01.01.2006, p. 119-132.

Research output: Contribution to journalArticle

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Rajtmajer SM, Miličević A, Trinajstić N, Randić M, Vukičević D. On the complexity of Archimedean solids. Journal of Mathematical Chemistry. 2006 Jan 1;39(1):119-132. https://doi.org/10.1007/s10910-005-9008-2