A note on the number of vertices of the Archimedean tiling

2018 ◽  
Vol 59 (1-2) ◽  
pp. 661-676
Author(s):  
Xianglin Wei ◽  
Weiqi Wang
Keyword(s):  
Soft Matter ◽  
2017 ◽  
Vol 13 (47) ◽  
pp. 8894-8902 ◽  
Author(s):  
Zdeněk Preisler ◽  
Barbara Saccà ◽  
Stephen Whitelam

DNA nanoparticles with three-fold coordination have been observed to self-assemble in experiment into a network equivalent to the hexagonal (6.6.6) tiling, and a network equivalent to the 4.8.8 Archimedean tiling.


2014 ◽  
Vol 27 (7) ◽  
pp. 075006 ◽  
Author(s):  
D Ray ◽  
C Reichhardt ◽  
C J Olson Reichhardt

2021 ◽  
Vol 10 (4) ◽  
pp. 2223-2233
Author(s):  
Salvatore Vassallo

In this paper we consider the snub hexagonal tiling of the plane ($(3^4, 6)$ Archimedean tiling) and compute the probability that a random circle or a random segment intersects a side of the tiling.


2005 ◽  
Vol 43 (18) ◽  
pp. 2427-2432 ◽  
Author(s):  
A. Takano ◽  
W. Kawashima ◽  
A. Noro ◽  
Y. Isono ◽  
N. Tanaka ◽  
...  

2006 ◽  
Vol 39 (14) ◽  
pp. 4869-4872 ◽  
Author(s):  
Kenichi Hayashida ◽  
Wataru Kawashima ◽  
Atsushi Takano ◽  
Yuya Shinohara ◽  
Yoshiyuki Amemiya ◽  
...  

2015 ◽  
Vol 6 (10) ◽  
pp. 5853-5858 ◽  
Author(s):  
Vladimir Stepanenko ◽  
Ramesh Kandanelli ◽  
Shinobu Uemura ◽  
Frank Würthner ◽  
Gustavo Fernández

A self-assembling Pd(ii) complex forms sophisticated concentration-dependent Archimedean tiling patterns composed of three types of polygons at the liquid/solid interface.


2017 ◽  
Vol 114 (46) ◽  
pp. 12132-12137 ◽  
Author(s):  
Zhi Wang ◽  
Hai-Feng Su ◽  
Yuan-Zhi Tan ◽  
Stan Schein ◽  
Shui-Chao Lin ◽  
...  

Buckminsterfullerene (C60) represents a perfect combination of geometry and molecular structural chemistry. It has inspired many creative ideas for building fullerene-like nanopolyhedra. These include other fullerenes, virus capsids, polyhedra based on DNA, and synthetic polynuclear metal clusters and cages. Indeed, the regular organization of large numbers of metal atoms into one highly complex structure remains one of the foremost challenges in supramolecular chemistry. Here we describe the design, synthesis, and characterization of a Ag180nanocage with 180 Ag atoms as 4-valent vertices (V), 360 edges (E), and 182 faces (F)––sixty 3-gons, ninety 4-gons, twelve 5-gons, and twenty 6-gons––in agreement with Euler’s rule V − E + F = 2. If each 3-gon (or silver Trigon) were replaced with a carbon atom linked by edges along the 4-gons, the result would be like C60, topologically a truncated icosahedron, an Archimedean solid with icosahedral (Ih) point-group symmetry. If C60can be described mathematically as a curling up of a 6.6.6 Platonic tiling, the Ag180cage can be described as a curling up of a 3.4.6.4 Archimedean tiling. High-resolution electrospray ionization mass spectrometry reveals that {Ag3}nsubunits coexist with the Ag180species in the assembly system before the final crystallization of Ag180, suggesting that the silver Trigon is the smallest building block in assembly of the final cage. Thus, we assign the underlying growth mechanism of Ag180to the Silver-Trigon Assembly Road (STAR), an assembly path that might be further employed to fabricate larger, elegant silver cages.


2018 ◽  
Vol 51 (19) ◽  
pp. 7807-7816 ◽  
Author(s):  
Faqiang Liu ◽  
Ping Tang ◽  
Hongdong Zhang ◽  
Yuliang Yang

2008 ◽  
Vol 20 (49) ◽  
pp. 494226 ◽  
Author(s):  
W Rżysko ◽  
A Patrykiejew ◽  
S Sokołowski

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