Polytope of Type {5,2,6,4,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,6,4,4}*1920
if this polytope has a name.
Group : SmallGroup(1920,205028)
Rank : 6
Schlafli Type : {5,2,6,4,4}
Number of vertices, edges, etc : 5, 5, 6, 12, 8, 4
Order of s₀s₁s₂s₃s₄s₅ : 60
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 : {5,2,6,2,4}*960, {5,2,6,4,2}*960a
   3-fold quotients : {5,2,2,4,4}*640
   4-fold quotients : {5,2,3,2,4}*480, {5,2,6,2,2}*480
   6-fold quotients : {5,2,2,2,4}*320, {5,2,2,4,2}*320
   8-fold quotients : {5,2,3,2,2}*240
   12-fold quotients : {5,2,2,2,2}*160
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope