Euclidean tilings by convex regular polygons: Difference between revisions

Content deleted Content added
Vaywatch (talk | contribs)
m Regular tilings: Adding notations
Vaywatch (talk | contribs)
m Adding notations
Line 53:
!colspan=6|p6m, *632
|- align=center valign=top
|[[File:1-uniform n4.svg|160px]]<br/><br/>[[File:Vertex type 3-12-12.svg|150x150px|alt=]]<br/>C&R: [[Truncated hexagonal tiling|3.12<sup>2</sup>]]<br/>GJ-H: [https://antwerp.hogg.io/?configuration=12-3%2Fm30%2Fr%28h3%29 12-3/m30/r(h3)]<br/>(''t'' = 2, ''e'' = 2)<br/>''t''{6,3}
|[[File:1-uniform n6.svg|160px]]<br/><br/>[[File:Vertex type 3-4-6-4.svg|100x100px|alt=]]<br/>C&R: [[Rhombitrihexagonal tiling|3.4.6.4]]<br/>GJ-H: [https://antwerp.hogg.io/?configuration=6-4-3%2Fm30%2Fr%28c2%29 6-4-3/m30/r(c2)]<br/>(''t'' = 3, ''e'' = 2)<br/>''rr''{3,6}
|[[File:1-uniform n3.svg|160px]]<br/><br/>[[File:Vertex type 4-6-12.svg|150x150px|alt=]]<br/>C&R: [[Truncated trihexagonal tiling|4.6.12]]<br/>GJ-H: [https://antwerp.hogg.io/?configuration=12-6%2C4%2Fm30%2Fr%28c2%29 12-6,4/m30/r(c2)]<br/>(''t'' = 3, ''e'' = 3)<br/>''tr''{3,6}
|[[File:1-uniform n7.svg|160px]]<br/><br/>[[File:Vertex type 3-6-3-6.svg|150x150px|alt=]]<br/>C&R: [[Trihexagonal tiling|(3.6)<sup>2</sup>]]<br/>GJ-H: [https://antwerp.hogg.io/?configuration=6-3-6%2Fm30%2Fr%28v4%29 6-3-6/m30/r(v4)]<br/>(''t'' = 2, ''e'' = 1)<br/>''r''{6,3}
|- align=center valign=top
|[[File:1-uniform n2.svg|160px]]<br/><br/>[[File:Vertex type 4-8-8.svg|150x150px|alt=]]<br/>C&R: [[Truncated square tiling|4.8<sup>2</sup>]]<br/>GJ-H: [https://antwerp.hogg.io/?configuration=8-4%2Fm90%2Fr%28h4%29 8-4/m90/r(h4)]<br/>(''t'' = 2, ''e'' = 2)<br/>''t''{4,4}
|[[File:1-uniform n9.svg|160px]]<br/><br/>[[File:Vertex type 3-3-4-3-4.svg|150x150px|alt=]]<br/>C&R: [[Snub square tiling|3<sup>2</sup>.4.3.4]]<br/>GJ-H: [https://antwerp.hogg.io/?configuration=4-3-3%2C4%2Fr90%2Fr%28h2%29 4-3-3,4/r90/r(h2)]<br/>(''t'' = 2, ''e'' = 2)<br/>''s''{4,4}
|[[File:1-uniform n8.svg|160px]]<br/><br/>[[File:Vertex type 3-3-3-4-4.svg|150x150px|alt=]]<br/>C&R: [[Elongated triangular tiling|3<sup>3</sup>.4<sup>2</sup>]]<br/>GJ-H: [https://antwerp.hogg.io/?configuration=4-3%2Fm90%2Fr%28h2%29 4-3/m90/r(h2)]<br/>(''t'' = 2, ''e'' = 3)<br/>{3,6}:''e''
|[[File:1-uniform n10.svg|160px]]<br/><br/>[[File:Vertex type 3-3-3-3-6.svg|150x150px|alt=]]<br/>C&R: [[Snub hexagonal tiling|3<sup>4</sup>.6]]<br/>GJ-H: [https://antwerp.hogg.io/?configuration=6-3-3%2Fr60%2Fr%28h5%29 6-3-3/r60/r(h5)]<br/>(''t'' = 3, ''e'' = 3)<br/>''sr''{3,6}
|}
''C&R: Cundy & Rollet's notation''<br/>
''GJ-H: Notation of GomJau-Hogg''<br/>
<br/>
Grünbaum and Shephard distinguish the description of these tilings as ''Archimedean'' as referring only to the local property of the arrangement of tiles around each vertex being the same, and that as ''uniform'' as referring to the global property of vertex-transitivity. Though these yield the same set of tilings in the plane, in other spaces there are Archimedean tilings which are not uniform.