Sphinx tiling

{{Short description|Type of tessallation}}

File:Self-replication of sphynx hexidiamonds.svg

In geometry, the sphinx tiling is a tessellation of the plane using the "sphinx", a pentagonal hexiamond formed by gluing six equilateral triangles together. The resultant shape is named for its reminiscence to the Great Sphinx at Giza. A sphinx can be dissected into any square number of copies of itself,{{citation

| last = Niţică | first = Viorel

| contribution = Rep-tiles revisited

| location = Providence, RI

| mr = 2027179

| pages = 205–217

| publisher = American Mathematical Society

| title = MASS selecta

| year = 2003}}. some of them mirror images, and repeating this process leads to a non-periodic tiling of the plane. The sphinx is therefore a rep-tile (a self-replicating tessellation).{{citation | last = Godrèche | first = C. | doi = 10.1088/0305-4470/22/24/006 | issue = 24 | journal = Journal of Physics A: Mathematical and General | mr = 1030678 | pages = L1163–L1166 | title = The sphinx: a limit-periodic tiling of the plane | volume = 22 | year = 1989}} It is one of few known pentagonal rep-tiles and is the only known pentagonal rep-tile whose sub-copies are equal in size.{{citation|contribution=The sphinx task centre problem|pages=371–378|first=Andy|last=Martin|title=The Changing Shape of Geometry|editor-first=Chris|editor-last=Pritchard|publisher=Cambridge University Press|year=2003|series=MAA Spectrum|isbn=9780521531627}}

{{multiple image | align=center

|image1 = Sphinx4.gif | caption1 = Dissection of the sphinx into four sub-copies

|image2 = Sphinx9.gif | caption2 = Dissection of the sphinx into nine sub-copies

}}