In[37]:=
  Rest[Union[Riemann80a /. FakeCyclicRule]]

Out[37]=

  {R     R    , R     R    , R     R    , R     R    , 
    afgh  bcde   agfh  bcde   aegh  bcdf   ageh  bcdf
   
    R     R    , R     R    , R     R    , R     R    , 
     aefh  bcdg   afeh  bcdg   aefg  bcdh   afeg  bcdh
   
    R     R    , R     R    , R     R    , R     R    , 
     adgh  bcef   agdh  bcef   adfh  bceg   afdh  bceg
   
    R     R    , R     R    , R     R    , R     R    , 
     adfg  bceh   afdg  bceh   adeh  bcfg   aedh  bcfg
   
    R     R    , R     R    , R     R    , R     R    , 
     adeg  bcfh   aedg  bcfh   adef  bcgh   aedf  bcgh
   
    R     R    , R     R    , R     R    , R     R    , 
     afgh  bdce   agfh  bdce   aegh  bdcf   ageh  bdcf
   
    R     R    , R     R    , R     R    , R     R    , 
     aefh  bdcg   afeh  bdcg   aefg  bdch   afeg  bdch
   
    R     R    , R     R    , R     R    , R     R    , 
     acgh  bdef   agch  bdef   acfh  bdeg   afch  bdeg
   
    R     R    , R     R    , R     R    , R     R    , 
     acfg  bdeh   afcg  bdeh   aceh  bdfg   aech  bdfg
   
    R     R    , R     R    , R     R    , R     R    , 
     aceg  bdfh   aecg  bdfh   acef  bdgh   aecf  bdgh
   
    R     R    , R     R    , R     R    , R     R    , 
     adgh  becf   agdh  becf   adfh  becg   afdh  becg
   
    R     R    , R     R    , R     R    , R     R    , 
     adfg  bech   afdg  bech   acgh  bedf   agch  bedf
   
    R     R    , R     R    , R     R    , R     R    , 
     acfh  bedg   afch  bedg   acfg  bedh   afcg  bedh
   
    R     R    , R     R    , R     R    , R     R    , 
     acdh  befg   adch  befg   acdg  befh   adcg  befh
   
    R     R    , R     R    , R     R    , R     R    , 
     acdf  begh   adcf  begh   adeh  bfcg   aedh  bfcg
   
    R     R    , R     R    , R     R    , R     R    , 
     adeg  bfch   aedg  bfch   aceh  bfdg   aech  bfdg
   
    R     R    , R     R    , R     R    , R     R    , 
     aceg  bfdh   aecg  bfdh   acdh  bfeg   adch  bfeg
   
    R     R    , R     R    , R     R    , R     R    , 
     acdg  bfeh   adcg  bfeh   acde  bfgh   adce  bfgh
   
    R     R    , R     R    , R     R    , R     R    , 
     adef  bgch   aedf  bgch   acef  bgdh   aecf  bgdh
   
    R     R    , R     R    , R     R    , R     R    , 
     acdf  bgeh   adcf  bgeh   acde  bgfh   adce  bgfh
   
    R     R    , R     R    , R     R    , R     R    , 
     abgh  cdef   agbh  cdef   abfh  cdeg   afbh  cdeg
   
    R     R    , R     R    , R     R    , R     R    , 
     abfg  cdeh   afbg  cdeh   abeh  cdfg   aebh  cdfg
   
    R     R    , R     R    , R     R    , R     R    , 
     abeg  cdfh   aebg  cdfh   abef  cdgh   aebf  cdgh
   
    R     R    , R     R    , R     R    , R     R    , 
     abgh  cedf   agbh  cedf   abfh  cedg   afbh  cedg
   
    R     R    , R     R    , R     R    , R     R    , 
     abfg  cedh   afbg  cedh   abdh  cefg   adbh  cefg
   
    R     R    , R     R    , R     R    , R     R    , 
     abdg  cefh   adbg  cefh   abdf  cegh   adbf  cegh
   
    R     R    , R     R    , R     R    , R     R    , 
     abeh  cfdg   aebh  cfdg   abeg  cfdh   aebg  cfdh
   
    R     R    , R     R    , R     R    , R     R    , 
     abdh  cfeg   adbh  cfeg   abdg  cfeh   adbg  cfeh
   
    R     R    , R     R    , R     R    , R     R    , 
     abde  cfgh   adbe  cfgh   abef  cgdh   aebf  cgdh
   
    R     R    , R     R    , R     R    , R     R    , 
     abdf  cgeh   adbf  cgeh   abde  cgfh   adbe  cgfh
   
    R     R    , R     R    , R     R    , R     R    , 
     abch  defg   acbh  defg   abcg  defh   acbg  defh
   
    R     R    , R     R    , R     R    , R     R    , 
     abcf  degh   acbf  degh   abch  dfeg   acbh  dfeg
   
    R     R    , R     R    , R     R    , R     R    , 
     abcg  dfeh   acbg  dfeh   abce  dfgh   acbe  dfgh
   
    R     R    , R     R    , R     R    , R     R    , 
     abcf  dgeh   acbf  dgeh   abce  dgfh   acbe  dgfh
   
    R     R    , R     R    , R     R    , R     R    }
     abcd  efgh   acbd  efgh   abcd  egfh   acbd  egfh

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