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- Complex_polytope abstract "In geometry, a complex polytope is a generalization of a polytope in real space to an analogous structure in a complex Hilbert space, where each real dimension is accompanied by an imaginary one. On a real line, two points bound a segment. This defines an edge with two bounding vertices. For a real polytope it is not possible to have a third vertex associated with an edge because one of them would then lie between the other two. On the complex line, which may be represented as an Argand diagram, points are not ordered and there is no idea of "between", so more than two vertex points may be associated with a given edge. Also, a real polygon has just two sides at each vertex, such that the boundary forms a closed loop. A real polyhedron has two faces at each edge such that the boundary forms a closed surface. A polychoron has two cells at each wall, and so on. These loops and surfaces have no analogy in complex spaces, for example a set of complex lines and points may form a closed chain of connections, but this chain does not bound a polygon. Thus, more than two elements meeting in one place may be allowed.Since bounding does not occur, we cannot think of a complex edge as a line segment, but as the whole line. Similarly, we cannot think of a bounded polygonal face but must accept the whole plane.Thus, a complex polytope may be understood as an arrangement of connected points, lines, planes and so on, where every point is the junction of multiple lines, every line of multiple planes, and so on. Likewise, each line must contain multiple points, each plane multiple lines, and so on.".
- Complex_polytope thumbnail ComplexOctagon.svg?width=300.
- Complex_polytope wikiPageID "8581934".
- Complex_polytope wikiPageLength "7231".
- Complex_polytope wikiPageOutDegree "24".
- Complex_polytope wikiPageRevisionID "681545921".
- Complex_polytope wikiPageWikiLink 4-polytope.
- Complex_polytope wikiPageWikiLink Argand_diagram.
- Complex_polytope wikiPageWikiLink Argument.
- Complex_polytope wikiPageWikiLink Arrangement_of_lines.
- Complex_polytope wikiPageWikiLink Category:Complex_analysis.
- Complex_polytope wikiPageWikiLink Category:Polytopes.
- Complex_polytope wikiPageWikiLink Complex_number.
- Complex_polytope wikiPageWikiLink Complex_plane.
- Complex_polytope wikiPageWikiLink Complex_reflection.
- Complex_polytope wikiPageWikiLink Complex_reflection_group.
- Complex_polytope wikiPageWikiLink Configuration_(geometry).
- Complex_polytope wikiPageWikiLink Geometry.
- Complex_polytope wikiPageWikiLink Harold_Scott_MacDonald_Coxeter.
- Complex_polytope wikiPageWikiLink Hilbert_space.
- Complex_polytope wikiPageWikiLink Imaginary_number.
- Complex_polytope wikiPageWikiLink Magnitude_(complex_number).
- Complex_polytope wikiPageWikiLink Polychoron.
- Complex_polytope wikiPageWikiLink Polytope.
- Complex_polytope wikiPageWikiLink Position_and_momentum_space.
- Complex_polytope wikiPageWikiLink Real_line.
- Complex_polytope wikiPageWikiLink Real_space.
- Complex_polytope wikiPageWikiLink Regular_polygon.
- Complex_polytope wikiPageWikiLink Regular_polytope.
- Complex_polytope wikiPageWikiLink Schläfli_symbol.
- Complex_polytope wikiPageWikiLink Tesseract.
- Complex_polytope wikiPageWikiLink File:ComplexOctagon.svg.
- Complex_polytope wikiPageWikiLinkText "Complex polytope".
- Complex_polytope wikiPageWikiLinkText "Complex polytope#Regular complex polytopes".
- Complex_polytope wikiPageWikiLinkText "complex polygon".
- Complex_polytope wikiPageWikiLinkText "complex polyhedra".
- Complex_polytope wikiPageWikiLinkText "complex polyhedron".
- Complex_polytope wikiPageWikiLinkText "complex polytope".
- Complex_polytope hasPhotoCollection Complex_polytope.
- Complex_polytope subject Category:Complex_analysis.
- Complex_polytope subject Category:Polytopes.
- Complex_polytope hypernym Generalization.
- Complex_polytope type Polytope.
- Complex_polytope type Space.
- Complex_polytope comment "In geometry, a complex polytope is a generalization of a polytope in real space to an analogous structure in a complex Hilbert space, where each real dimension is accompanied by an imaginary one. On a real line, two points bound a segment. This defines an edge with two bounding vertices. For a real polytope it is not possible to have a third vertex associated with an edge because one of them would then lie between the other two.".
- Complex_polytope label "Complex polytope".
- Complex_polytope sameAs Polytop.
- Complex_polytope sameAs Kompleksa_hiperpluredro.
- Complex_polytope sameAs m.0278swd.
- Complex_polytope sameAs Q1500531.
- Complex_polytope sameAs Q1500531.
- Complex_polytope wasDerivedFrom Complex_polytope?oldid=681545921.
- Complex_polytope depiction ComplexOctagon.svg.
- Complex_polytope isPrimaryTopicOf Complex_polytope.