1_32_polytope 1_32_polytope

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1 1_32 polytope

1.1 alternate names
1.2 construction
1.3 images
1.4 related polytopes , honeycombs





1_32 polytope


this polytope can tessellate 7-dimensional space, symbol 133, , coxeter-dynkin diagram, . voronoi cell of dual e7 lattice.


alternate names

emanuel lodewijk elte named v576 (for 576 vertices) in 1912 listing of semiregular polytopes.
coxeter called 132 bifurcating coxeter-dynkin diagram, single ring on end of 1-node branch.
pentacontihexa-hecatonicosihexa-exon (acronym lin) - 56-126 facetted polyexon (jonathan bowers)

construction

it created wythoff construction upon set of 7 hyperplane mirrors in 7-dimensional space.


the facet information can extracted coxeter-dynkin diagram,


removing node on end of 2-length branch leaves 6-demicube, 131,


removing node on end of 3-length branch leaves 122,


the vertex figure determined removing ringed node , ringing neighboring node. makes birectified 6-simplex, 032,


images

related polytopes , honeycombs

the 132 third in dimensional series of uniform polytopes , honeycombs, expressed coxeter 13k series. next figure euclidean honeycomb 133 , final noncompact hyperbolic honeycomb, 134.










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