Regular tessellations of maximally symmetric hyperbolic manifolds

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00581986" target="_blank" >RIV/67985840:_____/24:00581986 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.3390/sym16020141" target="_blank" >https://doi.org/10.3390/sym16020141</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/sym16020141" target="_blank" >10.3390/sym16020141</a>

Result language
angličtina
Original language name
Regular tessellations of maximally symmetric hyperbolic manifolds
Original language description
We first briefly summarize several well-known properties of regular tessellations of the three two-dimensional maximally symmetric manifolds, ????2, ????2, and ℍ2, by bounded regular tiles. For instance, there exist infinitely many regular tessellations of the hyperbolic plane ℍ2 by curved hyperbolic equilateral triangles whose vertex angles are 2????/???? for ????=7,8,9,… On the other hand, we prove that there is no curved hyperbolic regular tetrahedron which tessellates the three-dimensional hyperbolic space ℍ3. We also show that a regular tessellation of ℍ3 can only consist of the hyperbolic cubes, hyperbolic regular icosahedra, or two types of hyperbolic regular dodecahedra. There exist only two regular hyperbolic space-fillers of ℍ4. If ????>4, then there exists no regular tessellation of ℍ????.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA24-10586S" target="_blank" >GA24-10586S: Analytical and numerical modeling of hysteresis phenomena</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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