Polytope of Type {2,2,4,4,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,4,4}*512
if this polytope has a name.
Group : SmallGroup(512,7535005)
Rank : 6
Schlafli Type : {2,2,4,4,4}
Number of vertices, edges, etc : 2, 2, 4, 8, 8, 4
Order of s₀s₁s₂s₃s₄s₅ : 4
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 : {2,2,2,4,4}*256, {2,2,4,4,2}*256, {2,2,4,2,4}*256
   4-fold quotients : {2,2,2,2,4}*128, {2,2,2,4,2}*128, {2,2,4,2,2}*128
   8-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 5,13)( 6,14)( 7,15)( 8,16)( 9,17)(10,18)(11,19)(12,20)(21,29)(22,30)
(23,31)(24,32)(25,33)(26,34)(27,35)(28,36)(37,45)(38,46)(39,47)(40,48)(41,49)
(42,50)(43,51)(44,52)(53,61)(54,62)(55,63)(56,64)(57,65)(58,66)(59,67)
(60,68);;
s3 := (13,17)(14,18)(15,19)(16,20)(21,23)(22,24)(25,27)(26,28)(29,35)(30,36)
(31,33)(32,34)(37,41)(38,42)(39,43)(40,44)(53,59)(54,60)(55,57)(56,58)(61,63)
(62,64)(65,67)(66,68);;
s4 := ( 5,21)( 6,22)( 7,23)( 8,24)( 9,25)(10,26)(11,27)(12,28)(13,29)(14,30)
(15,31)(16,32)(17,33)(18,34)(19,35)(20,36)(37,53)(38,54)(39,55)(40,56)(41,57)
(42,58)(43,59)(44,60)(45,61)(46,62)(47,63)(48,64)(49,65)(50,66)(51,67)
(52,68);;
s5 := ( 5,45)( 6,46)( 7,47)( 8,48)( 9,49)(10,50)(11,51)(12,52)(13,37)(14,38)
(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,62)(22,61)(23,64)(24,63)(25,66)
(26,65)(27,68)(28,67)(29,54)(30,53)(31,56)(32,55)(33,58)(34,57)(35,60)
(36,59);;
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*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s3*s4*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(68)!(1,2);
s1 := Sym(68)!(3,4);
s2 := Sym(68)!( 5,13)( 6,14)( 7,15)( 8,16)( 9,17)(10,18)(11,19)(12,20)(21,29)
(22,30)(23,31)(24,32)(25,33)(26,34)(27,35)(28,36)(37,45)(38,46)(39,47)(40,48)
(41,49)(42,50)(43,51)(44,52)(53,61)(54,62)(55,63)(56,64)(57,65)(58,66)(59,67)
(60,68);
s3 := Sym(68)!(13,17)(14,18)(15,19)(16,20)(21,23)(22,24)(25,27)(26,28)(29,35)
(30,36)(31,33)(32,34)(37,41)(38,42)(39,43)(40,44)(53,59)(54,60)(55,57)(56,58)
(61,63)(62,64)(65,67)(66,68);
s4 := Sym(68)!( 5,21)( 6,22)( 7,23)( 8,24)( 9,25)(10,26)(11,27)(12,28)(13,29)
(14,30)(15,31)(16,32)(17,33)(18,34)(19,35)(20,36)(37,53)(38,54)(39,55)(40,56)
(41,57)(42,58)(43,59)(44,60)(45,61)(46,62)(47,63)(48,64)(49,65)(50,66)(51,67)
(52,68);
s5 := Sym(68)!( 5,45)( 6,46)( 7,47)( 8,48)( 9,49)(10,50)(11,51)(12,52)(13,37)
(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,62)(22,61)(23,64)(24,63)
(25,66)(26,65)(27,68)(28,67)(29,54)(30,53)(31,56)(32,55)(33,58)(34,57)(35,60)
(36,59);
poly := sub<Sym(68)|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*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5 >;

to this polytope