Four-Dimensional Regular Hexagon

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Defense date1984
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Abstract
On comprend facilement que les analogues quadridimensionnels du triangle régulier, du carré et du pentagone régulier (dans cet article, ils sont tous composes uniquement d’arêtes et ne comportent aucun élément à deux dimensions) sont respectivement le tétraèdre régulier, le cube et le dodécaèdre régulier (dans cet article, ils sont tous composés uniquement de faces et ne comportent aucun élément à trois dimensions). Alors, quel polyèdre est l’analogue quadridimensionnel de
I’hexagone régulier, c’est-à-dire un hexagone régulier quadridimensionnel? Si nous résolvons cette énigme, nous pourrons représenter un flocon de neige, un nid d’abeille, un crayon, etc. quadridimensionnels. It is easily understood that the Cdimensional analogues of the regular triangle, square, and regular pentagon (in this paper, all are composed of only edges and have no portion of 2-space) are the regular tetrahedron, cube, and regular dodecahedron (in this paper, all are composed of only faces and have no portion of 3-space) respectively. Then, which polyhedron is the Cdimensional analogue of the regular hexagon, i.e. Cdimensional regular hexagon? If this riddle is solved, we can see a 4-dimensional snowflake, honeycomb, pencil, etc.
CitationMiyazaki, Koji. "Four-Dimensional Regular Hexagon". Structural Topology, 1984, núm. 10
ISSN0226-9171
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