ORDER-3 HEPTAGONAL TILING

In geometry, the 'order-3 three heptagonal tiling' is a regular tiling of the hyperbolic plane. It has Schläfli symbol of ''{7,3}''.
The image shows a Poincaré disk model projection of the hyperbolic plane.
This tiling is topologically related as a part of sequence of regular polyhedra with vertex figure (n³).

(33)

(43)

(53)

(63) tiling

Contents

Wythoff constructions from heptagonal and triangular tilings

References

See also

External links

Wythoff constructions from heptagonal and triangular tilings

From a Wythoff construction there are eight hyperbolic uniform tilings that can be based from the regular heptagonal 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.
{| class="prettytable"
!Tiling
!Schläfli
symbol
!Wythoff
symbol
!Vertex
figure
!Image
|-
!Order-3 heptagonal tiling
|t₀{7,3}
| 3 | 7 2
|7³
|
|-
!Order-3 truncated heptagonal tiling
|t_0,1{7,3}
| 2 3 | 7
|3.14.14
|
|-
!Rectified order-3 heptagonal tiling
(Triheptagonal tiling)
|t₁{7,3}
| 2 | 7 3
|(3.7)²
|
|-
!Bitruncated order-3 heptagonal tiling
(Order-7 truncated triangular tiling)
|t_1,2{7,3}
| 2 7 | 3
|7.6.6
|
|-
!Order-7 triangular tiling
|t₂{7,3}
| 7 | 3 2
|3⁷
|
|-
!Cantellated order-3 heptagonal tiling
(Small rhombitriheptagonal tiling)
|t_0,2{7,3}
| 7 3 | 2
|3.4.7.4
|
|-
!Order-3 pmnitruncated heptagonal tiling
(Great rhombitriheptagonal tiling)
|t_0,1,2{7,3}
| 7 3 2 |
|4.7.14
|
|-
!Order-3 snub heptagonal tiling
|s{7,3}
|| 7 3 2
|3.3.3.3.7
|
|}

References

★

See also

★ hexagonal tiling

★ Tilings of regular polygons

★ List of uniform planar tilings

★ List of regular polytopes

External links

★

★

★ Hyperbolic and Spherical Tiling Gallery

★ KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings

★ Hyperbolic Planar Tessellations, Don Hatch