Questions?
See the FAQ
or other info.

Polytope of Type {6,6,6,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6,6,2,2}*1728g
if this polytope has a name.
Group : SmallGroup(1728,47915)
Rank : 6
Schlafli Type : {6,6,6,2,2}
Number of vertices, edges, etc : 6, 18, 18, 6, 2, 2
Order of s0s1s2s3s4s5 : 6
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,6,6,2,2}*864b
   3-fold quotients : {6,2,6,2,2}*576, {6,6,2,2,2}*576c
   6-fold quotients : {3,2,6,2,2}*288, {3,6,2,2,2}*288, {6,2,3,2,2}*288
   9-fold quotients : {2,2,6,2,2}*192, {6,2,2,2,2}*192
   12-fold quotients : {3,2,3,2,2}*144
   18-fold quotients : {2,2,3,2,2}*96, {3,2,2,2,2}*96
   27-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)(11,12)(13,16)(14,18)(15,17)(20,21)(22,25)
(23,27)(24,26)(29,30)(31,34)(32,36)(33,35)(38,39)(40,43)(41,45)(42,44)(47,48)
(49,52)(50,54)(51,53);;
s1 := ( 1,32)( 2,31)( 3,33)( 4,29)( 5,28)( 6,30)( 7,35)( 8,34)( 9,36)(10,41)
(11,40)(12,42)(13,38)(14,37)(15,39)(16,44)(17,43)(18,45)(19,50)(20,49)(21,51)
(22,47)(23,46)(24,48)(25,53)(26,52)(27,54);;
s2 := ( 2, 3)( 5, 6)( 8, 9)(10,19)(11,21)(12,20)(13,22)(14,24)(15,23)(16,25)
(17,27)(18,26)(29,30)(32,33)(35,36)(37,46)(38,48)(39,47)(40,49)(41,51)(42,50)
(43,52)(44,54)(45,53);;
s3 := ( 1,10)( 2,11)( 3,12)( 4,13)( 5,14)( 6,15)( 7,16)( 8,17)( 9,18)(28,37)
(29,38)(30,39)(31,40)(32,41)(33,42)(34,43)(35,44)(36,45);;
s4 := (55,56);;
s5 := (57,58);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(58)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)(11,12)(13,16)(14,18)(15,17)(20,21)
(22,25)(23,27)(24,26)(29,30)(31,34)(32,36)(33,35)(38,39)(40,43)(41,45)(42,44)
(47,48)(49,52)(50,54)(51,53);
s1 := Sym(58)!( 1,32)( 2,31)( 3,33)( 4,29)( 5,28)( 6,30)( 7,35)( 8,34)( 9,36)
(10,41)(11,40)(12,42)(13,38)(14,37)(15,39)(16,44)(17,43)(18,45)(19,50)(20,49)
(21,51)(22,47)(23,46)(24,48)(25,53)(26,52)(27,54);
s2 := Sym(58)!( 2, 3)( 5, 6)( 8, 9)(10,19)(11,21)(12,20)(13,22)(14,24)(15,23)
(16,25)(17,27)(18,26)(29,30)(32,33)(35,36)(37,46)(38,48)(39,47)(40,49)(41,51)
(42,50)(43,52)(44,54)(45,53);
s3 := Sym(58)!( 1,10)( 2,11)( 3,12)( 4,13)( 5,14)( 6,15)( 7,16)( 8,17)( 9,18)
(28,37)(29,38)(30,39)(31,40)(32,41)(33,42)(34,43)(35,44)(36,45);
s4 := Sym(58)!(55,56);
s5 := Sym(58)!(57,58);
poly := sub<Sym(58)|s0,s1,s2,s3,s4,s5>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

to this polytope