Polytope of Type {5,2,4,12,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,4,12,2}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240141)
Rank : 6
Schlafli Type : {5,2,4,12,2}
Number of vertices, edges, etc : 5, 5, 4, 24, 12, 2
Order of s₀s₁s₂s₃s₄s₅ : 60
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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 : {5,2,4,6,2}*960c
   4-fold quotients : {5,2,4,3,2}*480
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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