Polytope of Type {6,21,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,21,4}*1008
if this polytope has a name.
Group : SmallGroup(1008,903)
Rank : 4
Schlafli Type : {6,21,4}
Number of vertices, edges, etc : 6, 63, 42, 4
Order of s₀s₁s₂s₃ : 42
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   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) :
   3-fold quotients : {2,21,4}*336
   7-fold quotients : {6,3,4}*144
   21-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (29,57)(30,58)(31,59)(32,60)(33,61)(34,62)(35,63)(36,64)(37,65)(38,66)
(39,67)(40,68)(41,69)(42,70)(43,71)(44,72)(45,73)(46,74)(47,75)(48,76)(49,77)
(50,78)(51,79)(52,80)(53,81)(54,82)(55,83)(56,84);;
s1 := ( 1,29)( 2,30)( 3,32)( 4,31)( 5,53)( 6,54)( 7,56)( 8,55)( 9,49)(10,50)
(11,52)(12,51)(13,45)(14,46)(15,48)(16,47)(17,41)(18,42)(19,44)(20,43)(21,37)
(22,38)(23,40)(24,39)(25,33)(26,34)(27,36)(28,35)(59,60)(61,81)(62,82)(63,84)
(64,83)(65,77)(66,78)(67,80)(68,79)(69,73)(70,74)(71,76)(72,75);;
s2 := ( 1, 5)( 2, 8)( 3, 7)( 4, 6)( 9,25)(10,28)(11,27)(12,26)(13,21)(14,24)
(15,23)(16,22)(18,20)(29,61)(30,64)(31,63)(32,62)(33,57)(34,60)(35,59)(36,58)
(37,81)(38,84)(39,83)(40,82)(41,77)(42,80)(43,79)(44,78)(45,73)(46,76)(47,75)
(48,74)(49,69)(50,72)(51,71)(52,70)(53,65)(54,68)(55,67)(56,66);;
s3 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)
(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)
(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)(63,64)
(65,66)(67,68)(69,70)(71,72)(73,74)(75,76)(77,78)(79,80)(81,82)(83,84);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s2*s1*s3*s2*s3*s2*s1*s2, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(84)!(29,57)(30,58)(31,59)(32,60)(33,61)(34,62)(35,63)(36,64)(37,65)
(38,66)(39,67)(40,68)(41,69)(42,70)(43,71)(44,72)(45,73)(46,74)(47,75)(48,76)
(49,77)(50,78)(51,79)(52,80)(53,81)(54,82)(55,83)(56,84);
s1 := Sym(84)!( 1,29)( 2,30)( 3,32)( 4,31)( 5,53)( 6,54)( 7,56)( 8,55)( 9,49)
(10,50)(11,52)(12,51)(13,45)(14,46)(15,48)(16,47)(17,41)(18,42)(19,44)(20,43)
(21,37)(22,38)(23,40)(24,39)(25,33)(26,34)(27,36)(28,35)(59,60)(61,81)(62,82)
(63,84)(64,83)(65,77)(66,78)(67,80)(68,79)(69,73)(70,74)(71,76)(72,75);
s2 := Sym(84)!( 1, 5)( 2, 8)( 3, 7)( 4, 6)( 9,25)(10,28)(11,27)(12,26)(13,21)
(14,24)(15,23)(16,22)(18,20)(29,61)(30,64)(31,63)(32,62)(33,57)(34,60)(35,59)
(36,58)(37,81)(38,84)(39,83)(40,82)(41,77)(42,80)(43,79)(44,78)(45,73)(46,76)
(47,75)(48,74)(49,69)(50,72)(51,71)(52,70)(53,65)(54,68)(55,67)(56,66);
s3 := Sym(84)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)
(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)
(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)
(63,64)(65,66)(67,68)(69,70)(71,72)(73,74)(75,76)(77,78)(79,80)(81,82)(83,84);
poly := sub<Sym(84)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3, s3*s2*s1*s3*s2*s3*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope