Complex Uniform Tessellations on the Euclid Plane

Last update: 2003/09/13

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Complex Uniform Tessellations on the Euclid Plane

There are too complex special uniform tessellations on the Euclid plane.

[3,3,3,4,4], [3,3,3,4/3,4/3]
[3/2,Inf,3/2,Inf,3/2,4,4], [3/2,Inf,3/2,Inf,3/2,4/3,4/3]
[3/2,Inf,3/2,Inf,3/2,12/5,6,12/5], [3/2,Inf,3/2,Inf,3/2,12/7,6/5,12/7], [3/2,Inf,3/2,Inf,3/2,12,6/5,12], [3/2,Inf,3/2,Inf,3/2,12/11,6,12/11], [3/2,Inf,3/2,4/3,4/3,3/2,4/3,4/3], [3/2,Inf,3/2,4,4,3/2,4,4]
[3/2,Inf,3/2,4,4,3/2,4/3,4/3]
[4,Inf,4/3,8/3,4,8/3], [4,Inf,4/3,8,4/3,8], [4,Inf,4/3,8/3,8], [4,Inf,4/3,8,8/3]

[3,3,3,4,4], [3,3,3,4/3,4/3]
There are 2 complex uniform tessellations on the Euclid plane.

Vertex figure of [3,3,3,4,4]
Vertex figure of [3,3,3,4/3,4/3]

|2 2 (2|2)
[3,3,3,4,4]
[3,3,3,4/3,4/3]
[3/2,Inf,3/2,Inf,3/2,4,4], [3/2,Inf,3/2,Inf,3/2,4/3,4/3]
There are 2 complex uniform tessellations on the Euclid plane.

Vertex figure of
[3/2,Inf,3/2,Inf,3/2,4,4]
Vertex figure of
[3/2,Inf,3/2,Inf,3/2,4/3,4/3]

[3/2,Inf,3/2,Inf,3/2,4,4]
[3/2,Inf,3/2,Inf,3/2,4/3,4/3]

[3/2,Inf,3/2,Inf,3/2,12/5,6,12/5], [3/2,Inf,3/2,Inf,3/2,12/7,6/5,12/7], [3/2,Inf,3/2,Inf,3/2,12,6/5,12], [3/2,Inf,3/2,Inf,3/2,12/11,6,12/11], [3/2,Inf,3/2,4/3,4/3,3/2,4/3,4/3], [3/2,Inf,3/2,4,4,3/2,4,4]

There are 6 complex uniform tessellations on the Euclid plane. They have same vertexes with 6 Inf|6/5, 6/5 Inf|6, and 6 6/5 6/2|.

Vertex figure of <br>[3/2,Inf,3/2,Inf,3/2,12/5,6,12/5]
Vertex figure of
[3/2,Inf,3/2,Inf,3/2,12/5,6,12/5]
Vertex figure of
[3/2,Inf,3/2,Inf,3/2,12/7,6/5,12/7]

[3/2,Inf,3/2,Inf,3/2,12/5,6,12/5]
[3/2,Inf,3/2,Inf,3/2,12/7,6/5,12/7]

Vertex figure of
[3/2,Inf,3/2,Inf,3/2,12,6/5,12]
Vertex figure of
[3/2,Inf,3/2,Inf,3/2,12/11,6,12/11]

[3/2,Inf,3/2,Inf,3/2,12,6/5,12]
[3/2,Inf,3/2,Inf,3/2,12/11,6,12/11]

Vertex figure of
[3/2,Inf,3/2,4/3,4/3,3/2,4/3,4/3]
Vertex figure of
[3/2,Inf,3/2,4,4,3/2,4,4]

[3/2,Inf,3/2,4/3,4/3,3/2,4/3,4/3]
[3/2,Inf,3/2,4,4,3/2,4,4]

[3/2,Inf,3/2,4,4,3/2,4/3,4/3]
There is one complex uniform tessellations on the Euclid plane.

Vertex figure of
[3/2,Inf,3/2,4,4,3/2,4/3,4/3]

[3/2,Inf,3/2,4,4,3/2,4/3,4/3]

[4,Inf,4/3,8/3,4,8/3], [4,Inf,4/3,8,4/3,8], [4,Inf,4/3,8/3,8], [4,Inf,4/3,8,8/3]

There are 4 complex uniform tessellations on the Euclid plane. They have same vertexes with 4 Inf|4/3, 4/3 Inf|4, and 4 4/3 4/2|.

Vertex figure of [4,Inf,4/3,8/3,4,8/3]
Vertex figure of [4,Inf,4/3,8,4/3,8]

[4,Inf,4/3,8/3,4,8/3]
[4,Inf,4/3,8,4/3,8]

Vertex figure of [4,Inf,4/3,8/3,8]
Vertex figure of [4,Inf,4/3,8,8/3]

[4,Inf,4/3,8/3,8]
[4,Inf,4/3,8,8/3]

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Vertex figure of [3,3,3,4,4]	Vertex figure of [3,3,3,4/3,4/3]
\|2 2 (2\|2) [3,3,3,4,4]	[3,3,3,4/3,4/3]

Vertex figure of [3/2,Inf,3/2,Inf,3/2,4,4]	Vertex figure of [3/2,Inf,3/2,Inf,3/2,4/3,4/3]
[3/2,Inf,3/2,Inf,3/2,4,4]	[3/2,Inf,3/2,Inf,3/2,4/3,4/3]

Vertex figure of [3/2,Inf,3/2,Inf,3/2,12/5,6,12/5]	Vertex figure of [3/2,Inf,3/2,Inf,3/2,12/7,6/5,12/7]
[3/2,Inf,3/2,Inf,3/2,12/5,6,12/5]	[3/2,Inf,3/2,Inf,3/2,12/7,6/5,12/7]
Vertex figure of [3/2,Inf,3/2,Inf,3/2,12,6/5,12]	Vertex figure of [3/2,Inf,3/2,Inf,3/2,12/11,6,12/11]
[3/2,Inf,3/2,Inf,3/2,12,6/5,12]	[3/2,Inf,3/2,Inf,3/2,12/11,6,12/11]
Vertex figure of [3/2,Inf,3/2,4/3,4/3,3/2,4/3,4/3]	Vertex figure of [3/2,Inf,3/2,4,4,3/2,4,4]
[3/2,Inf,3/2,4/3,4/3,3/2,4/3,4/3]	[3/2,Inf,3/2,4,4,3/2,4,4]

Vertex figure of [4,Inf,4/3,8/3,4,8/3]	Vertex figure of [4,Inf,4/3,8,4/3,8]
[4,Inf,4/3,8/3,4,8/3]	[4,Inf,4/3,8,4/3,8]
Vertex figure of [4,Inf,4/3,8/3,8]	Vertex figure of [4,Inf,4/3,8,8/3]
[4,Inf,4/3,8/3,8]	[4,Inf,4/3,8,8/3]