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

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

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

Permutation Representation (Magma) :

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

to this polytope