Matches in SemOpenAlex for { <https://semopenalex.org/work/W2012251921> ?p ?o ?g. }
Showing items 1 to 78 of
78
with 100 items per page.
- W2012251921 endingPage "113514" @default.
- W2012251921 startingPage "113514" @default.
- W2012251921 abstract "We note that all regular and semiregular polytopes in arbitrary dimensions can be obtained from the Coxeter-Dynkin diagrams. The vertices of a regular or semiregular polytope are the weights obtained as the orbit of the Coxeter-Weyl group acting on the highest weight representing a selected irreducible representation of the Lie group. This paper, in particular, deals with the determination of the vertices of the Platonic and Archimedean solids from the Coxeter diagrams A3, B3, and H3 in the context of the quaternionic representations of the root systems and the Coxeter-Weyl groups. We use Lie algebraic techniques in the derivation of vertices of the polyhedra and show that the polyhedra possessing the tetrahedral, octahedral, and icosahedral symmetries are related to the Coxeter-Weyl groups representing the symmetries of the diagrams of A3, B3, and H3, respectively. This technique leads to the determination of the vertices of all Platonic and Archimedean solids except two chiral polyhedra, snubcuboctahedr..." @default.
- W2012251921 created "2016-06-24" @default.
- W2012251921 creator A5033021045 @default.
- W2012251921 creator A5044015111 @default.
- W2012251921 creator A5063602027 @default.
- W2012251921 date "2007-11-01" @default.
- W2012251921 modified "2023-09-27" @default.
- W2012251921 title "Polyhedra obtained from Coxeter groups and quaternions" @default.
- W2012251921 cites W11476871 @default.
- W2012251921 cites W1679856731 @default.
- W2012251921 cites W1978781889 @default.
- W2012251921 cites W1988619801 @default.
- W2012251921 cites W1993416406 @default.
- W2012251921 cites W1996229455 @default.
- W2012251921 cites W2071881521 @default.
- W2012251921 cites W2088790150 @default.
- W2012251921 cites W2102586619 @default.
- W2012251921 cites W2113203067 @default.
- W2012251921 cites W3124311860 @default.
- W2012251921 cites W3200596701 @default.
- W2012251921 cites W4247695726 @default.
- W2012251921 cites W4248660383 @default.
- W2012251921 cites W51037165 @default.
- W2012251921 doi "https://doi.org/10.1063/1.2809467" @default.
- W2012251921 hasPublicationYear "2007" @default.
- W2012251921 type Work @default.
- W2012251921 sameAs 2012251921 @default.
- W2012251921 citedByCount "21" @default.
- W2012251921 countsByYear W20122519212012 @default.
- W2012251921 countsByYear W20122519212013 @default.
- W2012251921 countsByYear W20122519212014 @default.
- W2012251921 countsByYear W20122519212015 @default.
- W2012251921 countsByYear W20122519212016 @default.
- W2012251921 countsByYear W20122519212017 @default.
- W2012251921 countsByYear W20122519212018 @default.
- W2012251921 countsByYear W20122519212019 @default.
- W2012251921 countsByYear W20122519212021 @default.
- W2012251921 crossrefType "journal-article" @default.
- W2012251921 hasAuthorship W2012251921A5033021045 @default.
- W2012251921 hasAuthorship W2012251921A5044015111 @default.
- W2012251921 hasAuthorship W2012251921A5063602027 @default.
- W2012251921 hasConcept C114614502 @default.
- W2012251921 hasConcept C143669375 @default.
- W2012251921 hasConcept C200127275 @default.
- W2012251921 hasConcept C202444582 @default.
- W2012251921 hasConcept C2524010 @default.
- W2012251921 hasConcept C33923547 @default.
- W2012251921 hasConcept C54829058 @default.
- W2012251921 hasConcept C57796230 @default.
- W2012251921 hasConceptScore W2012251921C114614502 @default.
- W2012251921 hasConceptScore W2012251921C143669375 @default.
- W2012251921 hasConceptScore W2012251921C200127275 @default.
- W2012251921 hasConceptScore W2012251921C202444582 @default.
- W2012251921 hasConceptScore W2012251921C2524010 @default.
- W2012251921 hasConceptScore W2012251921C33923547 @default.
- W2012251921 hasConceptScore W2012251921C54829058 @default.
- W2012251921 hasConceptScore W2012251921C57796230 @default.
- W2012251921 hasIssue "11" @default.
- W2012251921 hasLocation W20122519211 @default.
- W2012251921 hasOpenAccess W2012251921 @default.
- W2012251921 hasPrimaryLocation W20122519211 @default.
- W2012251921 hasRelatedWork W2067895084 @default.
- W2012251921 hasRelatedWork W2124464905 @default.
- W2012251921 hasRelatedWork W2276707593 @default.
- W2012251921 hasRelatedWork W2611438319 @default.
- W2012251921 hasRelatedWork W2762093594 @default.
- W2012251921 hasRelatedWork W2783989611 @default.
- W2012251921 hasRelatedWork W2950349561 @default.
- W2012251921 hasRelatedWork W2963138261 @default.
- W2012251921 hasRelatedWork W4292023742 @default.
- W2012251921 hasRelatedWork W1486016200 @default.
- W2012251921 hasVolume "48" @default.
- W2012251921 isParatext "false" @default.
- W2012251921 isRetracted "false" @default.
- W2012251921 magId "2012251921" @default.
- W2012251921 workType "article" @default.