Polytope of Type {42,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {42,12}*1008d
if this polytope has a name.
Group : SmallGroup(1008,903)
Rank : 3
Schlafli Type : {42,12}
Number of vertices, edges, etc : 42, 252, 12
Order of s₀s₁s₂ : 21
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {42,4}*336c
   6-fold quotients : {21,4}*168
   7-fold quotients : {6,12}*144d
   21-fold quotients : {6,4}*48b
   42-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(84)!( 3, 4)( 5,25)( 6,26)( 7,28)( 8,27)( 9,21)(10,22)(11,24)(12,23)
(13,17)(14,18)(15,20)(16,19)(31,32)(33,53)(34,54)(35,56)(36,55)(37,49)(38,50)
(39,52)(40,51)(41,45)(42,46)(43,48)(44,47)(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);
s1 := 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);
s2 := Sym(84)!( 1,30)( 2,29)( 3,32)( 4,31)( 5,34)( 6,33)( 7,36)( 8,35)( 9,38)
(10,37)(11,40)(12,39)(13,42)(14,41)(15,44)(16,43)(17,46)(18,45)(19,48)(20,47)
(21,50)(22,49)(23,52)(24,51)(25,54)(26,53)(27,56)(28,55)(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>;

Finitely Presented Group Representation (Magma) :

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

References : None.
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