Content deleted Content added
Added free to read link in citations with OAbot #oabot |
m Open access bot: hdl updated in citation with #oabot. |
||
Line 17:
However, this notation has two main problems related to ambiguous conformation and uniqueness <ref name="Gomez-Jauregui 2012">{{cite journal |last1=Gomez-Jauregui |first1=Valentin al.|last2=Otero |first2=Cesar |display-authors=etal |title=Generation and Nomenclature of Tessellations and Double-Layer Grids |journal=Journal of Structural Engineering |date=2012 |volume=138 |issue=7 |pages=843–852 |doi=10.1061/(ASCE)ST.1943-541X.0000532 |hdl=10902/5869 |url=https://ascelibrary.org/doi/10.1061/%28ASCE%29ST.1943-541X.0000532|hdl-access=free }}</ref> First, when it comes to k-uniform tilings, the notation does not explain the relationships between the vertices. This makes it impossible to generate a covered plane given the notation alone. And second, some tessellations have the same nomenclature, they are very similar but it can be noticed that the relative positions of the hexagons are different. Therefore, the second problem is that this nomenclature is not unique for each tessellation.
In order to solve those problems, GomJau-Hogg’s notation <ref>{{cite journal |last1=Gomez-Jauregui |first1=Valentin |last2=Hogg |first2=Harrison|display-authors=etal |title=GomJau-Hogg's Notation for Automatic Generation of k-Uniform Tessellations with ANTWERP v3.0 |journal=Symmetry |date=2021 |volume=13 |issue=12 |page=2376 |doi=10.3390/sym13122376 |bibcode=2021Symm...13.2376G |doi-access=free |hdl=10902/23907 |hdl-access=free }}</ref> is a slightly modified version of the research and notation presented in 2012,<ref name="Gomez-Jauregui 2012" /> about the generation and nomenclature of tessellations and double-layer grids. Antwerp v3.0,<ref>{{cite web |last1=Hogg |first1=Harrison |last2=Gomez-Jauregui |first2=Valentin |title=Antwerp 3.0 |url=https://antwerp.hogg.io/<}}</ref> a free online application, allows for the infinite generation of regular polygon tilings through a set of shape placement stages and iterative rotation and reflection operations, obtained directly from the GomJau-Hogg’s notation.
== Regular tilings ==
| |||