lc cutters: pentagonal tilling
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LC CUTTERSPentagonal tiling
LC Cutters Polygons sets
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LC Cutters Polygons set 1 (1-5)
LC Cutters Polygons set 3 (11-15)
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Order at LC Store EU or LC Store USA.
LC Cutters Polygons set 2 (6-10)
LC Cutters Polygons set 4 (16-20)
Pentagonal tilingFrom Wikipedia, the free encyclopedia
source: www.wikipedia.org/wiki/Pentagonal_tiling
Monohedral convex pentagonal tilings
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In geometry, a pentagonal tiling is a tiling of the plane where each individual piece is in the shape of a specific pentagon.
A regular pentagonal tiling on the Euclidean plane is impossible because the internal angle of a regular pentagon, 108°, is not a divisor of 360°, the angle measure of a whole turn.
Fifteen types of convex pentagons are known to tile the plane monohedrally (i.e. with one type of tile).[1] The most recent one was discovered in 2015. It is not known whether this list is complete.[2] Bagina (2011) showed that there are only eight edge-to-edge convex types, a result obtained independently by Sugimoto (2012).
Each enumerated tiling family contains pentagons that belong to no other type; however, some individual pentagons may belong to multiple types. In addition, some of the pentagons in the known tiling types also permit alternative tiling patterns beyond the standard tiling exhibited by all members of its type.
Reinhardt (1918)
Reinhardt (1918) found the first five types of pentagonal tile. All five can create isohedral tilings, meaning that the symmetries of the tiling can take any tile to any other tile (more formally, the automorphism group acts transitively on the tiles).
#1 #6
#2 #7
#3 #8
#4 #9
#5 #10
#11 #16
#12 #17
#13 #18
#14 #19
#15 #20
LC CUTTER: Pentagon #1Order at LC Store EU or LC Store USA.
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LC CUTTER: Pentagon #2 Order at LC Store EU or LC Store USA.
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LC CUTTER: Pentagon #3Order at LC Store EU or LC Store USA.
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LC MINI SLICER
LC CUTTER: Pentagon #4Order at LC Store EU or LC Store USA.
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LC CUTTER: Pentagon #5Order at LC Store EU or LC Store USA.
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LC CUTTER: Pentagon #6Order at LC Store EU or LC Store USA.
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LC CUTTER: Pentagon #7Order at LC Store EU or LC Store USA.
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LC CUTTER: Pentagon #8Order at LC Store EU or LC Store USA.
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LC CUTTER: Pentagon #9Order at LC Store EU or LC Store USA.
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LC CUTTER: Pentagon #10Order at LC Store EU or LC Store USA.
Making a pattern with LC CUTTER #10
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LC CUTTER: Pentagon #11Order at LC Store EU or LC Store USA.
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LC CUTTER: Pentagon #12Order at LC Store EU or LC Store USA.
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LC CUTTER: Pentagon #13Order at LC Store EU or LC Store USA.
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LC SLICER
LC CUTTER: Pentagon #14Order at LC Store EU or LC Store USA.
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LC CUTTER: Pentagon #15Order at LC Store EU or LC Store USA.
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LC CUTTER: Pentagon #16Order at LC Store EU or LC Store USA.
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LC CUTTER: Pentagon #17Order at LC Store EU or LC Store USA.
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LC CUTTER: Pentagon #18Order at LC Store EU or LC Store USA.
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LC CUTTER: Pentagon #19Order at LC Store EU or LC Store USA.
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LC CUTTER: Pentagon #20Order at LC Store EU or LC Store USA.
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