File:Monohedral pentagonal tiling 4, 1, 1(M), T100 (1).png

English: One of a series of monohedral pentagonal tiling patterns – tilings of the plane that are composed of identical pentagonal tiles (allowing mirror image tiles).

General information about this series of files:

Colouring of static images (png files). Tiles that are equivalent under translation/rotation are coloured the same. Almost all tiling patterns in this series incorporate asymmetrical tiles (not superimposable on their mirror image). These are designated “right-handed” or “left-handed”. Right-handed colours are:

rh₁ = yellow, rh₂ = dark blue, rh₃ = dark red, rh₄ = dark grey, rh₅ = dark purple, rh₆ = dark brown, rh₇ = dark turquoise rh₈ = dark cream

Left-handed colours are:

lh₁ = green, lh₂ = light blue, lh₃ = light red, lh₄ = light grey, lh₅ = light purple, lh₆ = light brown, lh₇ = light turquoise, lh₈ = light cream

The most frequent handedness within the repeating cell of the tiling pattern is designated right-handed, and the other (if any) left-handed, or if there are the same number of tiles of each handedness then this choice is made arbitrarily. If the tiling pattern as a whole is symmetrical (superimposable on its mirror image, with appropriate translation/rotation), then the colours used are rh₁ … rh_n and lh₁ … lh_n, where the tiles coloured lh_i are the mirrors of rh_i (for example, green tiles are the mirrors of yellow, light blue tiles are the mirrors of dark blue, and so on). Otherwise, the colours are rh₁ … rh_n and, if any left-handed tiles, lh_n+1 … lh_m, for appropriate n and m.

In the infrequent case (in this series) of symmetrical tiles, these are coloured right-handed, unless additional tile equivalences arise under reflection of the whole tiling, in which case right- and left-handed mirror colours are used as for asymmetrical tiles. In the latter case, if a symmetrical tile maps to itself on reflection then the “right-handed” colour is used.

File names. Files are named “monohedral pentagonal tiling cell_size, num_rh_colours, num_lh_colours, Ttypes (seq)”, where cell_size is the number of tiles in the minimal repeating cell. num_rh_colours and num_lh_colours are respectively the number of different right-handed and left-handed colours in the tiling, as described above. num_lh_colours may be zero. “(M)” after num_lh_colours denotes that the left-handed tiles mirror the right-handed in the pairs yellow – green, dark blue – light blue, etc., as described above. types is the tile type(s). Tile types 1 through 15 are as explained at https://en.wikipedia.org/wiki/Pentagonal_tiling. Type 100 has adjacent vertices summing to 360 degrees. Types 101 through 111 are various types in which non-adjacent vertices sum to 360 degrees. seq is a sequence number to differentiate file names that would otherwise be identical; this is present as “(1)” even if there is only one file of that name.

Animated images (gif files). These are provided when the tiling pattern allows one or more degrees of freedom; they show a representative range of tile shapes. These are coloured for aesthetic reasons only. Apart from the extension, the animated file name is the same as the corresponding static file. The file name parameters apply to the general case for the pattern, and individual special cases that the animation may pass through may differ (for example, may satisfy additional types).