Talk:Prototile
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for congruent you need more than a top. space. --MarSch 15:50, 16 Jun 2005 (UTC)
Meaning - prototile, shape, tile
[edit]In the first sentence it says:
"..a prototile is one of the shapes of a tile in a tessellation."
This is not so clear as there are several words that the reader don't even know are defined or not. The word "prototile" as one of the "shapes" indicates that prototiles are made of shapes. I doubt this is the case, and regardless, the word "shape" needs to be explained too.
The sentence continues by saying that the shape is part of a "tile", which makes me confused. Here the opposite is claimed - that prototiles are part of "tiles", that is if prototiles and tiles are the same thing. This needs to be sorted out, and if they aren't the same, the situation needs to be explained further too.
When I searched for some information about this I came across this excerpt by Judith Cederberg in the publication "A Course in Modern Geometries" (https://books.google.com/books?id=Fo9tqL99jdMC&pg=PA174#v=onepage&q&f=false):
"A tiling, or tessellation, of the plane is a covering of the plane with congruent copies of one or more prototiles so there are no gaps or overlaps (except at edges). Copies of the prototiles are called tiles and a point at which three or more tiles meet is called a vertex of the tiling."
Besides the word "congruent" this phrasing is much more easy to understand.