Polytope of Type {8,8,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,8,2,2}*512b
if this polytope has a name.
Group : SmallGroup(512,6255213)
Rank : 5
Schlafli Type : {8,8,2,2}
Number of vertices, edges, etc : 8, 32, 8, 2, 2
Order of s₀s₁s₂s₃s₄ : 8
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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 : {4,8,2,2}*256a, {8,4,2,2}*256a
   4-fold quotients : {4,4,2,2}*128, {2,8,2,2}*128, {8,2,2,2}*128
   8-fold quotients : {2,4,2,2}*64, {4,2,2,2}*64
   16-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope