User:Double sharp/List of uniform polytera by Goursat pentachoron

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NO, DOUBLE SHARP, YOU ARE NOT STARTING ON A 5D VERSION WITHOUT HAVING FINISHED THE 4D VERSION, ESPECIALLY WHEN SO MUCH IS LEFT UNDONE AND BESIDES YOU'RE JUST GOING TO ABANDON THIS ONE TOO...

  • voice in head silenced*

The 5D version of List of uniform polyhedra by Schwarz triangle and List of uniform polychora by Goursat tetrahedron. Klitzing is used as the source.

O voice in my head with perpetual Caps Lock turned on, dost thou not know me and my spirit of taking things too far? Be grateful I haven't yet started List of uniform polypeta by Goursat hexateron.

O other voice in my head who speaks with eternal italics, do note that you have just given me an idea.

Darn.

Bwa ha ha ha.

  • o3o3o3o3o (hixic, hexateron symmetry)
  • o3o3o3o4o (pentic, penteract symmetry)
  • o3o3o *b3o3o (hinnic, demipenteractic symmetry)
  • o3o3o3o3o3/2*c (example nonconvex, along with below...)
  • o3o3o3o4/3o
  • o3o3o3o4o4/3*c
  • o3o3o3o4/3o4*c
  • o3o3o3o *b4o4/3*c
  • o4/3o4o3*a3o3/2o3*a
  • prismatics
  • possibly non-Wythoffian nonconvex? (not actually known whether Wythoffian or not)

Convex[edit]

Nonprismatic[edit]

CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
o3o3o3o3o
CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
o3o3o3o4o
CDel nodes.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
o3o3o *b3o3o
quasiregular

CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png – Hexateron (hix)
CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png – Rectified hexateron (rix)
CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png – Dodecateron (dot)

Prismatic[edit]

Non-Wythoffian[edit]

Nonconvex[edit]

1251 nonprismatic uniform polytera are currently known: of these, only 58 are convex. It is unknown whether the set is complete, or even which of them may be found by Wythoff construction and which cannot. Below, only a few cases are presented as examples.

Nonprismatic[edit]

    3   3   3     
 o---o---o---o   
      3/2 \ / 3  
         o   

o3o3o3o3o3/2*c

   3   3   3   3  4/3   
 o---o---o---o---o---o  

o3o3o3o4/3o

   3   3   3    
 o---o---o---o  
4 \ / 4/3    
o

o3o3o3o4o4/3*c

   3   3   3      
 o---o---o---o    
        4 \ / 4/3 
        o   

o3o3o3o4/3o4*c

   3   3   3      
 o---o---o---o    
    4 \ / 4/3     
   o      

o3o3o3o *b4o4/3*c

  3/2     
 o---o    
3 \ / 3   
   o      
3 / \ 4/3 
 o---o    
   4  

o4/3o4o3*a3o3/2o3*a

Prismatic[edit]

Non-Wythoffian[edit]

References[edit]

Richard Klitzing: