33344-33434 tiling

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{| class=wikitable style="float:right;" width="360"
! style="background-color:#e7dcc3;" colspan=3|33344-33434 tilings
|-
| style="text-align:center;" colspan=3|[[File:2-uniform_n16.svg|160px]][[File:2-uniform_n17.svg|160px]]<BR>Faced colored by their symmetry positions
|-
| style="background-color:#e7dcc3;width:105px;" |Type||colspan=2|[[2-uniform tiling]]
|-
| style="background-color:#e7dcc3;width:105px;"|Designation||[3³.4²; 3².4.3.4]₁||[3³.4²; 3².4.3.4]₂
|-
| style="background-color:#e7dcc3;" |[[Vertex configuration]]s||colspan=2|3.3.4.3.4 and 3.3.3.4.4
|-
| style="background-color:#e7dcc3;" |[[List of planar symmetry groups#Wallpaper groups|Symmetry]]||p4g, [4,4⁺], (4*2)||pgg, [4⁺,4⁺], (22×)
|-
| style="background-color:#e7dcc3;" |Rotation symmetry||p4, [4,4]⁺, (442)||p2, [4⁺,4⁺]⁺, (2222)
|-
| style="background-color:#e7dcc3;" |Properties||4-[[isohedral]], 5-[[isotoxal]]||3-[[isohedral]], 6-[[isotoxal]]
|}
In [[geometry]] of the Euclidean plane, a '''33344-33434 tiling''' is one of two of 20 [[2-uniform tiling]]s of the [[Euclidean plane]] [[Tiling by regular polygons|by regular polygons]]. They contains regular [[triangle]] and [[square]] faces, arranged in two [[vertex configuration]]: 3.3.3.4.4 and 3.3.4.3.4.<ref>Chavey (1989)</ref>

The first has triangles in groups of 3 and square in groups of 1 and 2. It has 4 types of faces and 5 types of edges.

The second has triangles in groups of 4, and squares in groups of 2. It has 3 types of face and 6 types of edges.

== Geometry==
Its two [[vertex configuration]]s are shared with two 1-uniform tilings:
{| class=wikitable
|- align=center
|[[File:snub square tiling vertfig.png|60px]]<BR>3.3.4.3.4
|[[File:Tiling_33344-vertfig.png|60px]]<BR>3.3.3.4.4
|- align=center
|[[File:1-uniform_n8.svg|160px]]<BR>[[elongated triangular tiling]]
|[[File:1-uniform_n9.svg|160px]]<BR>[[snub square tiling]]
|}

=== Dual tilings===
The dual tilings have [[right triangle]] and [[Kite (geometry)|kite]] faces, defined by [[face configuration]]s: V3.3.3.4.4 and V3.3.4.3.4, and can be seen combining the [[prismatic pentagonal tiling]] and [[Cairo pentagonal tiling]]s.
{| class=wikitable
!Faces||colspan=2|1-uniform||colspan=2|2-uniform
|- valign=bottom align=center
|[[File:Tiling face 3-3-3-4-4.svg|60px]]<BR>V3.3.3.4.4<BR>[[File:Tiling face 3-3-4-3-4.svg|80px]]<BR>V3.3.4.3.4
|[[File:1-uniform 8 dual.svg|160px]]<BR>prismatic pentagonal tiling
|[[File:1-uniform_9_dual.svg|160px]]<BR>Cairo pentagonal tiling
|[[File:2-uniform 16 dual.svg|160px]]<BR>Dual tiling I
|[[File:2-uniform 17 dual.svg|160px]]<BR>Dual tiling II
|}

==Notes==


== References==
* Keith Critchlow, ''Order in Space: A design source book'', 1970, pp.&nbsp;62–67
* Ghyka, M. ''The Geometry of Art and Life'', (1946), 2nd edition, New York: Dover, 1977. Demiregular tiling #15
* pp.&nbsp;35–43
* Liquid error: wrong number of arguments (1 for 2) p.&nbsp;65-67
* ''Sacred Geometry Design Sourcebook: Universal Dimensional Patterns'', Bruce Rawles, 1997. pp.&nbsp;36–37 [https://ift.tt/2TybZZH]
* ''Introduction to Tessellations, Dale Seymour, Jill Britton, (1989), p.57, Fig 3-24 ''Tessellations of regular polygons that contain more than one type of vertex point''
== External links ==
*
*
*
* [https://ift.tt/2Ttq2Q6 In Search of Demiregular Tilings], Helmer Aslaksen
* [https://ift.tt/2IRksmq ''n''-uniform tilings] Brian Galebach, [https://ift.tt/2TmCKA9 2-Uniform Tiling 1 of 20]

[[Category:Euclidean plane geometry]]
[[Category:Tessellation]]

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