Polytope of Type {6,28}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,28}*504
if this polytope has a name.
Group : SmallGroup(504,169)
Rank : 3
Schlafli Type : {6,28}
Number of vertices, edges, etc : 9, 126, 42
Order of s₀s₁s₂ : 28
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,28,2} of size 1008
Vertex Figure Of :
   {2,6,28} of size 1008
Quotients (Maximal Quotients in Boldface) :
   7-fold quotients : {6,4}*72
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,28}*1008
   3-fold covers : {6,28}*1512, {6,84}*1512a, {6,84}*1512b, {6,84}*1512c
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

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

References : None.
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