Rhombitrihexagonal Tiling - Related Polyhedra and Tilings

Related Polyhedra and Tilings

There are eight uniform tilings that can be based from the regular hexagonal tiling (or the dual triangular tiling). Drawing the tiles colored as red on the original faces, yellow at the original vertices, and blue along the original edges, there are 8 forms, 7 which are topologically distinct. (The truncated triangular tiling is topologically identical to the hexagonal tiling.)

Uniform hexagonal/triangular tilings
Symmetry:, (*632) +, (632) , (*333) , (3*3)
{6,3} t0,1{6,3} t1{6,3} t1,2{6,3} t2{6,3} t0,2{6,3} t0,1,2{6,3} s{6,3} h{6,3} h1,2{6,3}
Uniform duals
V6.6.6 V3.12.12 V3.6.3.6 V6.6.6 V3.3.3.3.3.3 V3.4.12.4 V.4.6.12 V3.3.3.3.6 V3.3.3.3.3.3

This tiling is topologically related as a part of sequence of cantellated polyhedra with vertex figure (3.4.n.4), and continues as tilings of the hyperbolic plane. These vertex-transitive figures have (*n32) reflectional symmetry.

Dimensional family of expanded polyhedra and tilings: 3.4.n.4
Symmetry
*n32
 Spherical Planar Hyperbolic...
*232

D3h		 *332

Td		 *432

Oh		 *532

Ih		 *632

P6m		 *732

 *832
...
 *∞32
Expanded
figure
3.4.2.4
3.4.3.4
3.4.4.4
3.4.5.4
3.4.6.4
3.4.7.4
3.4.8.4
3.4.∞.4
Coxeter
Schläfli
t0,2{2,3}
t0,2{3,3}
t0,2{4,3}
t0,2{5,3}
t0,2{6,3}
t0,2{7,3}
t0,2{8,3}
t0,2{∞,3}
Deltoidal figure
V3.4.2.4
V3.4.3.4
V3.4.4.4
V3.4.5.4
V3.4.6.4
V3.4.7.4
V3.4.8.4
V3.4.∞.4
Coxeter

The hexagonal cupola contains the pattern of this tiling, but closes it into a degenerate polygon with a dodecagon base.

Family of cupolae
2 3 4 5 6

Digonal cupola
Triangular cupola
Square cupola
Pentagonal cupola
Hexagonal cupola
(Flat)

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