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Polytope of Type {28,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {28,6}*504
if this polytope has a name.
Group : SmallGroup(504,169)
Rank : 3
Schlafli Type : {28,6}
Number of vertices, edges, etc : 42, 126, 9
Order of s0s1s2 : 28
Order of s0s1s2s1 : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {28,6,2} of size 1008
Vertex Figure Of :
   {2,28,6} of size 1008
Quotients (Maximal Quotients in Boldface) :
   7-fold quotients : {4,6}*72
Covers (Minimal Covers in Boldface) :
   2-fold covers : {28,6}*1008
   3-fold covers : {28,6}*1512, {84,6}*1512a, {84,6}*1512b, {84,6}*1512c
Permutation Representation (GAP) :
s0 := ( 2, 7)( 3, 6)( 4, 5)( 8,22)( 9,28)(10,27)(11,26)(12,25)(13,24)(14,23)
(15,43)(16,49)(17,48)(18,47)(19,46)(20,45)(21,44)(30,35)(31,34)(32,33)(36,50)
(37,56)(38,55)(39,54)(40,53)(41,52)(42,51)(58,63)(59,62)(60,61);;
s1 := ( 1, 2)( 3, 7)( 4, 6)( 8,16)( 9,15)(10,21)(11,20)(12,19)(13,18)(14,17)
(22,23)(24,28)(25,27)(29,37)(30,36)(31,42)(32,41)(33,40)(34,39)(35,38)(43,44)
(45,49)(46,48)(50,58)(51,57)(52,63)(53,62)(54,61)(55,60)(56,59);;
s2 := ( 1,29)( 2,30)( 3,31)( 4,32)( 5,33)( 6,34)( 7,35)( 8,22)( 9,23)(10,24)
(11,25)(12,26)(13,27)(14,28)(15,36)(16,37)(17,38)(18,39)(19,40)(20,41)(21,42)
(43,50)(44,51)(45,52)(46,53)(47,54)(48,55)(49,56);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(63)!( 2, 7)( 3, 6)( 4, 5)( 8,22)( 9,28)(10,27)(11,26)(12,25)(13,24)
(14,23)(15,43)(16,49)(17,48)(18,47)(19,46)(20,45)(21,44)(30,35)(31,34)(32,33)
(36,50)(37,56)(38,55)(39,54)(40,53)(41,52)(42,51)(58,63)(59,62)(60,61);
s1 := Sym(63)!( 1, 2)( 3, 7)( 4, 6)( 8,16)( 9,15)(10,21)(11,20)(12,19)(13,18)
(14,17)(22,23)(24,28)(25,27)(29,37)(30,36)(31,42)(32,41)(33,40)(34,39)(35,38)
(43,44)(45,49)(46,48)(50,58)(51,57)(52,63)(53,62)(54,61)(55,60)(56,59);
s2 := Sym(63)!( 1,29)( 2,30)( 3,31)( 4,32)( 5,33)( 6,34)( 7,35)( 8,22)( 9,23)
(10,24)(11,25)(12,26)(13,27)(14,28)(15,36)(16,37)(17,38)(18,39)(19,40)(20,41)
(21,42)(43,50)(44,51)(45,52)(46,53)(47,54)(48,55)(49,56);
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1 >; 
 
References : None.
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