BEING  THE  EIEST  CLASS  OF  E-GONOHS  X-EDEA. 
157 
Both  these  are  of  the  first  class  of  4-gonous  polyedra,  the  only  one  besides  of  this  class 
being  the  autopolar  6-acral  6-edron.  This  is, — 
'^134^235  43323486  354:33g4:i 
4:i343235  82434:335  43328435  344i4i36  85438641? 
which  is  also  thus  represented,  using  the  circles  123456,  123456,  and  putting  A for  the 
gamic  of  «,  &c., — 
which  reduces  by  the  gamic  pair  Ee  to  the  pyramid  on  1234. 
The  fom’th  and  fifth  are  a sympolar  pair,  a 6-acral  7-edron,  and  a 7-acral  6-edron,  of 
the  second  class  of  4-gonous  ;r-edra,  made  by  partitioning  a 4-gon  or  a 4-ace  in  the  pre- 
ceding autopolar  so  as  to  introduce  no  pentace  or  pentagon.  Thus, 
» 
4i32324i  3243'334i  3344344i  3^443536  35443g45  3g433745 
37824145  37433282  33433g44  4j4i3436  44863545? 
4i32324i  82438344  83448444  84448536  85448645  86438745 
37324i45  87438232  83438644  4i44343g  4i363545? 
both  which  are  seen  in  the  paradigm  made  by  the  circles  1234567  and  123456,  as 
follows : — 
The  sixth  and  seventh  are  the  regular  6-edron  and  its  polar  syntyp  the  regular  8-edron, 
both  of  the  second  class,  the  first  represented  by  writing  under  3434  the  12  quadruplets 
1426  2435  3443  4153  5263  6275  7286  8116  1144  8251  3365  7625, 
and  the  second  by  writing  under  3434  the  same  12  quadruplets.  Both  are  exhibited 
