Piecewise-linear embeddings of decussate extended θ graphs and tetrahedra.
Acta Crystallogr A Found Adv
; 78(Pt 6): 498-506, 2022 Nov 01.
Article
de En
| MEDLINE
| ID: mdl-36318071
ABSTRACT
An nθ graph is an n-valent graph with two vertices. From symmetry considerations, it has vertex-edge transitivity 1â
1. Here, they are considered extended with divalent vertices added to the edges to explore the simplest piecewise-linear tangled embeddings with straight, non-intersecting edges (sticks). The simplest tangles found are those with 3n sticks, transitivity 2â
2, and with 2â(n - 1)/2â ambient-anisotopic tangles. The simplest finite and 1-, 2- and 3-periodic decussate structures (links and tangles) are described. These include finite cubic and icosahedral and 1- and 3-periodic links, all with minimal transitivity. The paper also presents the simplest tangles of extended tetrahedra and their linkages to form periodic polycatenanes. A vertex- and edge-transitive embedding of a tangled srs net with tangled and polycatenated θ graphs and vertex-transitive tangled diamond (dia) nets are described.
Texte intégral:
1
Collection:
01-internacional
Base de données:
MEDLINE
Langue:
En
Journal:
Acta Crystallogr A Found Adv
Année:
2022
Type de document:
Article
Pays d'affiliation:
États-Unis d'Amérique