TRIHEXAGONAL TILING

In geometry, the 'trihexagonal tiling' is a semiregular tiling of the Euclidean plane. There are two triangles and two hexagons alternating on each vertex. It has Schläfli symbol of ''t₁{6,3}''.
There are 3 regular and 8 semiregular tilings in the plane.
There are two distinct uniform colorings of a trihexagonal tiling. (Naming the colors by indices on the 3 hexagons around a vertex (3.6.3.6): 1212, 1232.)

Contents

Related polyhedra and tilings

See also

References

Related polyhedra and tilings

This tiling is topologically related as a part of sequence of rectified polyhedra with vertex figure (3.n.3.n). In this sequence, the edges project into great circles of a sphere on the polyhedra and infinite lines in the planar tiling.

(3.3.3.3)	(3.4.3.4)	(3.5.3.5)
(3.6.3.6)	(3.7.3.7)	(3.8.3.8)

And 3-colors with even orders: ''3.2n.3.2n'':

(3.4.3.4)

(3.6.3.6)

(3.8.3.8)

See also

★ Tilings of regular polygons

★ List of uniform tilings

★ Kagome lattice

References

★ Tilings and Patterns, Grünbaum, Branko ; and Shephard, G. C., , , W. H. Freeman, 1987, ISBN 0-716-71193-1 (Chapter 2.1: ''Regular and uniform tilings'', p.58-65)

★ Williams, Robert ''The Geometrical Foundation of Natural Structure: A Source Book of Design'' New York: Dover, 1979. p38