Geodesic
Some Possible and Some Impossible Tripartitions of the Plane
Canadian mathematical bulletin, Tome 11 (1968) no. 3, pp. 415-421

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For each positive integer n it is possible to partition the Euclidean plane into n (disjoint) congruent connected sets [1], but if n > 2, it is impossible to partition the plane into n congruent continuumwise connected sets such that some one of the sets can be translated onto another one [2]. This paper is concerned with the possibility of partitioning the plane into three congruent sets without any topological restrictions whatever. 
Meyers, Leroy F. Some Possible and Some Impossible Tripartitions of the Plane. Canadian mathematical bulletin, Tome 11 (1968) no. 3, pp. 415-421. doi: 10.4153/CMB-1968-048-4
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     title = {Some {Possible} and {Some} {Impossible} {Tripartitions} of the {Plane}},
     journal = {Canadian mathematical bulletin},
     pages = {415--421},
     year = {1968},
     volume = {11},
     number = {3},
     doi = {10.4153/CMB-1968-048-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1968-048-4/}
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