Polytope of Type {5,2,8,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,8,8}*1280a
if this polytope has a name.
Group : SmallGroup(1280,145169)
Rank : 5
Schlafli Type : {5,2,8,8}
Number of vertices, edges, etc : 5, 5, 8, 32, 8
Order of s₀s₁s₂s₃s₄ : 40
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 : {5,2,4,8}*640a, {5,2,8,4}*640b
   4-fold quotients : {5,2,4,4}*320, {5,2,2,8}*320
   8-fold quotients : {5,2,2,4}*160, {5,2,4,2}*160
   16-fold quotients : {5,2,2,2}*80
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := ( 6,22)( 7,23)( 8,24)( 9,25)(10,27)(11,26)(12,29)(13,28)(14,31)(15,30)
(16,33)(17,32)(18,34)(19,35)(20,36)(21,37)(38,54)(39,55)(40,56)(41,57)(42,59)
(43,58)(44,61)(45,60)(46,63)(47,62)(48,65)(49,64)(50,66)(51,67)(52,68)
(53,69);;
s3 := (10,11)(12,13)(14,16)(15,17)(18,21)(19,20)(22,26)(23,27)(24,28)(25,29)
(30,36)(31,37)(32,34)(33,35)(38,46)(39,47)(40,48)(41,49)(42,51)(43,50)(44,53)
(45,52)(54,67)(55,66)(56,69)(57,68)(58,63)(59,62)(60,65)(61,64);;
s4 := ( 6,38)( 7,39)( 8,40)( 9,41)(10,43)(11,42)(12,45)(13,44)(14,48)(15,49)
(16,46)(17,47)(18,53)(19,52)(20,51)(21,50)(22,54)(23,55)(24,56)(25,57)(26,59)
(27,58)(28,61)(29,60)(30,64)(31,65)(32,62)(33,63)(34,69)(35,68)(36,67)
(37,66);;
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, 
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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(69)!(2,3)(4,5);
s1 := Sym(69)!(1,2)(3,4);
s2 := Sym(69)!( 6,22)( 7,23)( 8,24)( 9,25)(10,27)(11,26)(12,29)(13,28)(14,31)
(15,30)(16,33)(17,32)(18,34)(19,35)(20,36)(21,37)(38,54)(39,55)(40,56)(41,57)
(42,59)(43,58)(44,61)(45,60)(46,63)(47,62)(48,65)(49,64)(50,66)(51,67)(52,68)
(53,69);
s3 := Sym(69)!(10,11)(12,13)(14,16)(15,17)(18,21)(19,20)(22,26)(23,27)(24,28)
(25,29)(30,36)(31,37)(32,34)(33,35)(38,46)(39,47)(40,48)(41,49)(42,51)(43,50)
(44,53)(45,52)(54,67)(55,66)(56,69)(57,68)(58,63)(59,62)(60,65)(61,64);
s4 := Sym(69)!( 6,38)( 7,39)( 8,40)( 9,41)(10,43)(11,42)(12,45)(13,44)(14,48)
(15,49)(16,46)(17,47)(18,53)(19,52)(20,51)(21,50)(22,54)(23,55)(24,56)(25,57)
(26,59)(27,58)(28,61)(29,60)(30,64)(31,65)(32,62)(33,63)(34,69)(35,68)(36,67)
(37,66);
poly := sub<Sym(69)|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, 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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 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