On the nonexistence of k-reptile tetrahedra

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F11%3A10100601" target="_blank" >RIV/00216208:11320/11:10100601 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s00454-011-9334-z" target="_blank" >http://dx.doi.org/10.1007/s00454-011-9334-z</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00454-011-9334-z" target="_blank" >10.1007/s00454-011-9334-z</a>

Result language
angličtina
Original language name
On the nonexistence of k-reptile tetrahedra
Original language description
A d-dimensional simplex S is called a k-reptile if it can be tiled without overlaps by simplices S_1, S_2,..., S_k that are all congruent and similar to S. For d=2, k-reptile simplices (triangles) exist for many values of k and they have been completelycharacterized by Snover, Waiveris, and Williams. On the other hand, for d greater than 2, only one construction of k-reptile simplices is known, the Hill simplices, and it provides only k of the form m^d, m = 2, 3,.... We prove that for d greater than 2,k-reptile simplices (tetrahedra) exist only for k=m^3. This partially confirms a conjecture of Hertel, asserting that the only k-reptile tetrahedra are the Hill tetrahedra.
Czech name
—
Czech description
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Project
<a href="/en/project/1M0545" target="_blank" >1M0545: Institute for Theoretical Computer Science</a>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP) Z - Vyzkumny zamer (s odkazem do CEZ) S - Specificky vyzkum na vysokych skolach

Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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