Triangular tiling: Difference between revisions

Revision as of 14:25, 20 September 2024

Latest revision as of 10:12, 29 August 2025

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|BGCOLOR="#c0c0ff"|111112(*)

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|[[File:Uniform triangular tiling 111111.pngsvg|75px]]

|[[File:Uniform triangular tiling 121212.pngsvg|75px]]

|[[File:Uniform triangular tiling 111222.pngsvg|75px]]

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|p6m (*632)

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== A2 lattice and circle packings ==

{{distinguish|Strukturbericht designation#A-compounds{{!}}the A2 crystal lattice structure in the Strukturbericht classification system}}

[[File:Compound 3 triangular tilings.pngsvg|thumb|The A{{sup sub|*|2}} lattice as three triangular tilings: {{CDD|node_1|split1|branch}} + {{CDD|node|split1|branch_10lu}} + {{CDD|node|split1|branch_01ld}}]]

The [[vertex arrangement]] of the triangular tiling is called an [[Root system#Explicit construction of the irreducible root systems|A₂ lattice]].<ref>{{Cite web|url=http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/A2.html|title = The Lattice A2}}</ref> It is the 2-dimensional case of a [[simplectic honeycomb]].

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<gallery>

Isohedral_tiling_p3-11.pngsvg|[[Scalene triangle]]<BR/>p2 symmetry

Isohedral_tiling_p3-12.svg|Scalene triangle<BR/>pmg symmetry

Isohedral_tiling_p3-13.svg|[[Isosceles triangle]]<BR/>cmm symmetry

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|[[File:Tetrakishexahedron.jpg|60px]]<BR/>[[Tetrakis hexahedron|V4.6.6]]

|[[File:Pentakisdodecahedron.jpg|60px]]<BR/>[[Pentakis dodecahedron|V5.6.6]]

|[[File:Uniform polyhedron-63-t2.pngsvg|60px]]<BR/>V6.6.6

|[[File:Heptakis heptagonal tiling.svg|60px]]<BR/>[[Order-7 truncated triangular tiling|V7.6.6]]

|}

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{| class=wikitable

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