Relevant bibliographies by topics / Regular polytopes

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Regular polytopes'

Author: Grafiati
Published: 10 March 2023

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Journal articles on the topic "Regular polytopes"

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Lalvani, Haresh. "Higher Dimensional Periodic Table Of Regular And Semi-Regular Polytopes." International Journal of Space Structures 11, no. 1-2 (1996): 155–71. http://dx.doi.org/10.1177/026635119601-222.

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This paper presents a higher-dimensional periodic table of regular and semi-regular n-dimensional polytopes. For regular n-dimensional polytopes, designated by their Schlafli symbol {p,q,r,…u,v,w}, the table is an (n-1)-dimensional hypercubic lattice in which each polytope occupies a different vertex of the lattice. The values of p,q,r,…u,v,w also establish the corresponding n-dimensional Cartesian co-ordinates (p,q,r,…u,v,w) of their respective positions in the hypercubic lattice. The table is exhaustive and includes all known regular polytopes in Euclidean, spherical and hyperbolic spaces, i
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Schulte, Egon, and Asia Ivić Weiss. "Free Extensions of Chiral Polytopes." Canadian Journal of Mathematics 47, no. 3 (1995): 641–54. http://dx.doi.org/10.4153/cjm-1995-033-7.

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AbstractAbstract polytopes are discrete geometric structures which generalize the classical notion of a convex polytope. Chiral polytopes are those abstract polytopes which have maximal symmetry by rotation, in contrast to the abstract regular polytopes which have maximal symmetry by reflection. Chirality is a fascinating phenomenon which does not occur in the classical theory. The paper proves the following general extension result for chiral polytopes. If 𝒦 is a chiral polytope with regular facets 𝓕 then among all chiral polytopes with facets 𝒦 there is a universal such polytope 𝓟, whose gro
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CONNOR, THOMAS, DIMITRI LEEMANS, and MARK MIXER. "ABSTRACT REGULAR POLYTOPES FOR THE O'NAN GROUP." International Journal of Algebra and Computation 24, no. 01 (2014): 59–68. http://dx.doi.org/10.1142/s0218196714500052.

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In this paper, we consider how the O'Nan sporadic simple group acts as the automorphism group of an abstract regular polytope. In particular, we prove that there is no regular polytope of rank at least five with automorphism group isomorphic to O′N. Moreover, we classify all rank four regular polytopes having O′N as their automorphism group.
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Comes, Jonathan. "Regular Polytopes." Mathematics Enthusiast 1, no. 2 (2004): 30–37. http://dx.doi.org/10.54870/1551-3440.1007.

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Hou, Dong-Dong, Yan-Quan Feng та Dimitri Leemans. "Existence of regular 3-polytopes of order 2𝑛". Journal of Group Theory 22, № 4 (2019): 579–616. http://dx.doi.org/10.1515/jgth-2018-0155.

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AbstractIn this paper, we prove that for any positive integers {n,s,t} such that {n\geq 10}, {s,t\geq 2} and {n-1\geq s+t}, there exists a regular polytope with Schläfli type {\{2^{s},2^{t}\}} and its automorphism group is of order {2^{n}}. Furthermore, we classify regular polytopes with automorphism groups of order {2^{n}} and Schläfli types {\{4,2^{n-3}\},\{4,2^{n-4}\}} and {\{4,2^{n-5}\}}, therefore giving a partial answer to a problem proposed by Schulte and Weiss in [Problems on polytopes, their groups, and realizations, Period. Math. Hungar. 53 2006, 1–2, 231–255].
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Boya, Luis J., and Cristian Rivera. "On Regular Polytopes." Reports on Mathematical Physics 71, no. 2 (2013): 149–61. http://dx.doi.org/10.1016/s0034-4877(13)60026-9.

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Cuypers, Hans. "Regular quaternionic polytopes." Linear Algebra and its Applications 226-228 (September 1995): 311–29. http://dx.doi.org/10.1016/0024-3795(95)00149-l.

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McMullen, Peter, and Egon Schulte. "Flat regular polytopes." Annals of Combinatorics 1, no. 1 (1997): 261–78. http://dx.doi.org/10.1007/bf02558480.

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Coxeter, H. S. M. "Regular and semi-regular polytopes. II." Mathematische Zeitschrift 188, no. 4 (1985): 559–91. http://dx.doi.org/10.1007/bf01161657.

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Coxeter, H. S. M. "Regular and semi-regular polytopes. III." Mathematische Zeitschrift 200, no. 1 (1988): 3–45. http://dx.doi.org/10.1007/bf01161745.

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Dissertations / Theses on the topic "Regular polytopes"

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Duke, Helene. "A Study of the Rigidity of Regular Polytopes." The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1366271197.

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Beteto, Marco Antonio Leite. "Less conservative conditions for the robust and Gain-Scheduled LQR-state derivative controllers design /." Ilha Solteira, 2019. http://hdl.handle.net/11449/180976.

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Orientador: Edvaldo Assunção<br>Resumo: Neste trabalho é proposta a resolução do problema do regulador linear quadrático (Linear Quadratic Regulator - LQR) via desigualdades matriciais lineares (Linear Matrix Inequalities - LMIs) para sistemas lineares e invariantes no tempo sujeitos a incertezas politópicas, bem como para sistemas lineares sujeitos a parâmetros variantes no tempo (Linear Parameter Varying - LPV). O projeto dos controladores é baseado na realimentação derivativa. A escolha da realimentação derivativa se dá devido à sua fácil implementação em certas aplicações como, por exemplo
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Bruni, Matteo. "Incremental Learning of Stationary Representations." Doctoral thesis, 2021. http://hdl.handle.net/2158/1237986.

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Humans and animals, during their life, continuously acquire new knowledge over time while making new experiences. They learn new concepts without forgetting what already learned, they typically use a few training examples (i.e. a child could recognize a giraffe after seeing a single picture) and they are able to discern what is known from what is unknown (i.e. unknown faces). In contrast, current supervised learning systems, work under the assumption that all data is known and available during learning, training is performed offline and a test dataset is typically required. What is missin
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Books on the topic "Regular polytopes"

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Coxeter, H. S. M. Regular complex polytopes. 2nd ed. Cambridge University Press, 1991.

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Chang, Peter Chung Yuen. Quantum field theory on regular polytopes. University of Manchester, 1993.

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Mostly surfaces. American Mathematical Society, 2011.

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Coxeter, H. S. M. Regular Polytopes. Dover Publications, Incorporated, 2012.

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Coxeter, H. S. M. Regular Polytopes. Dover Publications, Incorporated, 2012.

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Coxeter, H. S. M. Regular Polytopes. Dover Publications, 2013.

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Doran, B., Egon Schulte, M. Ismail, Peter McMullen, and G. C. Rota. Abstract Regular Polytopes. Cambridge University Press, 2004.

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Mcmullen, Peter, and Egon Schulte. Abstract Regular Polytopes. Cambridge University Press, 2002.

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9

McMullen, Peter. Geometric Regular Polytopes. University of Cambridge ESOL Examinations, 2020.

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Schulte, Egon, and Peter McMullen. Abstract Regular Polytopes. Cambridge University Press, 2009.

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Book chapters on the topic "Regular polytopes"

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Johnson, D. L. "Regular Polytopes." In Springer Undergraduate Mathematics Series. Springer London, 2001. http://dx.doi.org/10.1007/978-1-4471-0243-4_12.

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McMullen, Peter. "Rigidity of Regular Polytopes." In Rigidity and Symmetry. Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4939-0781-6_13.

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McMullen, Peter. "Modern Developments in Regular Polytopes." In Polytopes: Abstract, Convex and Computational. Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-0924-6_5.

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Lee, C. "Regular triangulations of convex polytopes." In DIMACS Series in Discrete Mathematics and Theoretical Computer Science. American Mathematical Society, 1991. http://dx.doi.org/10.1090/dimacs/004/35.

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De Loera, Jesús A., Jörg Rambau, and Francisco Santos. "Regular Triangulations and Secondary Polytopes." In Triangulations. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-12971-1_5.

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Schulte, Egon. "Classification of Locally Toroidal Regular Polytopes." In Polytopes: Abstract, Convex and Computational. Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-0924-6_6.

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McMullen, Peter. "New Regular Compounds of 4-Polytopes." In Bolyai Society Mathematical Studies. Springer Berlin Heidelberg, 2018. http://dx.doi.org/10.1007/978-3-662-57413-3_12.

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Schulte, Egon. "Regular Incidence Complexes, Polytopes, and C-Groups." In Discrete Geometry and Symmetry. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-78434-2_18.

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Downs, Martin, and Gareth A. Jones. "Möbius Inversion in Suzuki Groups and Enumeration of Regular Objects." In Symmetries in Graphs, Maps, and Polytopes. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-30451-9_5.

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Banchoff, Thomas F. "Torus Decompostions of Regular Polytopes in 4-space." In Shaping Space. Springer New York, 2012. http://dx.doi.org/10.1007/978-0-387-92714-5_20.

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Conference papers on the topic "Regular polytopes"

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Shahid, Salman, Sakti Pramanik, and Charles B. Owen. "Minimum bounding boxes for regular cross-polytopes." In the 27th Annual ACM Symposium. ACM Press, 2012. http://dx.doi.org/10.1145/2245276.2245447.

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Bueno, Jose Nuno A. D., Kaio D. T. Rocha, Lucas B. Marcos, and Marco H. Terra. "Mode-Independent Regulator for Polytopic Markov Jump Linear Systems*." In 2022 30th Mediterranean Conference on Control and Automation (MED). IEEE, 2022. http://dx.doi.org/10.1109/med54222.2022.9837134.

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