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Regular polytope

In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry. In particular, all its elements or j-faces (for all 0 ≤ j ≤ n, where n is the dimension of the polytope) — cells, faces and so on — are also transitive on the symmetries of the polytope, and are themselves…

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Regular polytope

Nodes179
Edges178
Triples179
Avg. degree1.99
Density0.011173
Components1

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Regular polytope

Top relations

related to Bibliography · 107
Regular polytope → Abstract Regular Polytopes, American Journal, Applied Mathematics, Arnold, Artmann, Augustin-Louis, Barnes, Benno, Cambridge University Press, Cauchy, Colloquium Internationale CNRS, Complexes, Concepts, Courier Dover, Coxeter, Cromwell, Crystallography, David, Deloudi, Denkschriften
related to Higher-dimensional polytopes · 15
Regular polytope → Alicia Boole Stott, Between, CITEREFSchläfli1858, Coxeter, English, Five, His, It, Ludwig Schläfli, Platonic, Reinhold Hoppe, Schläfli, Schläfli's, Swiss, The
related to Apeirotopes — infinite polytopes · 11
Regular polytope → Branko Grünbaum, Coxeter, He, In, It, More, Nowadays, Petrie, Since, The, They
related to Star polygons and polyhedra · 11
Regular polytope → Augustin Cauchy, Bradwardinus, Euclid, Johannes Kepler, Kepler-Poinsot, Louis Poinsot, Renaissance, The, These, Thomas Bradwardine, Various
related to Classification by Coxeter groups · 6
Regular polytope → Coxeter, Coxeter-Dynkin, Regular, Reversing, The, These
related to Schläfli symbols · 5
Regular polytope → Ludwig Schläfli, Platonic, So, The, This
related to Description · 4
Regular polytope → In, Regular, The, There
related to Duality of the regular polytopes · 3
Regular polytope → For, The, The Schläfli
related to External links · 3
Regular polytope → List, Small Regular Polytopes, The Atlas
see also · 3
Regular polytope → Leendert, List, Waerden

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Important terminology

regular polytopes polytope dimensions abstract symmetry faces vertex one polyhedra displaystyle example polygons form cube schläfli may coxeter isbn figure

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Regular polytopeis apolytope whose symmetry group acts transitively on its flags0.90text
Regular polytopeis adual of the dual polytope's facet0.90text
Arthur Cayleyinstance ofmathematicians0.80text
Ludwig Schläfli had developed the theory of regular polytopes in fourinstance ofmathematicians0.80text
higher dimensionsinstance ofmathematicians0.80text
such as the tesseractinstance ofmathematicians0.80text
the 24-cell.The latter are difficultinstance ofmathematicians0.80text
the 57-cell or the 11-cellinstance ofcan be directly visualised and depicted using 4-dimensional stereographs.Harder still to imagine are the more modern abstract regular polytopes0.80text
the one shown can already give some limited insight into the structure of the polytope.Another way a three-dimensional viewer can comprehend the structure of a four-dimensional polytope is through beinginstance ofeven a simple animation0.80text
Regular polytoperelated to Apeirotopes — infinite polytopesIn0.60section
Regular polytoperelated to Apeirotopes — infinite polytopesCoxeter0.60section
Regular polytoperelated to Apeirotopes — infinite polytopesPetrie0.60section

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