Geodesic
Sets Homothetic to their Intersection with a Translate
Canadian mathematical bulletin, Tome 18 (1975) no. 5, pp. 739-748

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Inspired by a question of J. B. Miller, L. Fejes Tóth asked for a catalogue of those subsets of Euclidean n-space which are homothetic (similar and similarly situated) to their intersection with a suitably translated copy of themselves. For example, a triangle is homothetic to its intersection with an arbitrarily translated replica provided only that the intersection has non-void interior. In 3-space a cube is homothetic to its intersection with a replica translated part way along any body diagonal. With these two preliminary examples for motivation, let us make a definition. 
Wilker, J. B. Sets Homothetic to their Intersection with a Translate. Canadian mathematical bulletin, Tome 18 (1975) no. 5, pp. 739-748. doi: 10.4153/CMB-1975-128-5
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     title = {Sets {Homothetic} to their {Intersection} with a {Translate}},
     journal = {Canadian mathematical bulletin},
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     year = {1975},
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     number = {5},
     doi = {10.4153/CMB-1975-128-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-128-5/}
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