Triangular tiling

Triangular tiling
Dimensionality	E2 tiling
Schläfli Symbol	'"`UNIQ--postMath-00000001-QINU`"'
Bowers acronym	trat
Subfacets
Vertices	ℵ0 points
Edges	ℵ0 line segments
Faces	ℵ0 triangles
Cells	1 triangular tiling

The triangular tiling is a regular tiling formed from a plane filled with triangles. Six triangles join at each vertex. Its Bowers acronym is trat.

Structure and Sections

This tiling can also be given a coloring where the triangles have alternating colors around a vertex. This is the base of the 3-3-3 triangle group.

Subfacets

• ℵ₀ points (0D)
• ℵ₀ line segments (1D)
• ℵ₀ triangles (2D)
• 1 triangular tiling (E² tiling)

See also

$\{2,6\}$	$\{3,6\}$	$\{4,6\}$	$\{5,6\}$	$\{6,6\}$	$\{7,6\}$	$\{8,6\}$	...	$\{\infty,6\}$	$\{\frac{\pi i}{\lambda},6\}$
Hexagonal hosohedron	Triangular tiling	Order-6 square tiling	Order-6 pentagonal tiling	Order-6 hexagonal tiling	Order-6 heptagonal tiling	Order-6 octagonal tiling	...	Order-6 apeirogonal tiling	Order-6 pseudogonal tiling

$\{3,2\}$	$\{3, 3\}$	$\{3, 4\}$	$\{3, 5\}$	$\{3,6\}$	$\{3,7\}$	$\{3,8\}$	...	$\{3,\infty\}$	$\{3,\frac{\pi i}{\lambda}\}$
Trigonal dihedron	Tetrahedron	Octahedron	Icosahedron	Triangular tiling	Order-7 triangular tiling	Order-8 triangular tiling	...	Infinite-order triangular tiling	Imaginary-order triangular tiling

Regular $t_0 \{6,3\}$	Rectified $t_1 \{6,3\}$	Birectified $t_2 \{6,3\}$	Truncated $t_{0,1} \{6,3\}$	Bitruncated $t_{1,2} \{6,3\}$	Cantellated $t_{0,2} \{6,3\}$	Cantitruncated $t_{0,1,2} \{6,3\}$
Hexagonal tiling	Trihexagonal tiling	Triangular tiling	Truncated hexagonal tiling	Hexagonal tiling	Rhombitrihexagonal tiling	Omnitruncated trihexagonal tiling

Regular $t_0 \{(3,3,3,)\}$	Rectified $t_1 \{(3,3,3,)\}$	Birectified $t_2 \{(3,3,3,)\}$	Truncated $t_{0,1} \{(3,3,3,)\}$	Bitruncated $t_{1,2} \{(3,3,3,)\}$	Cantellated $t_{0,2} \{(3,3,3,)\}$	Cantitruncated $t_{0,1,2} \{(3,3,3,)\}$
Triangular tiling	Triangular tiling	Triangular tiling	Trihexagonal tiling	Trihexagonal tiling	Trihexagonal tiling	Hexagonal tiling