Polytope of Type {3,2,6,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,6,12}*1152b
if this polytope has a name.
Group : SmallGroup(1152,157603)
Rank : 5
Schlafli Type : {3,2,6,12}
Number of vertices, edges, etc : 3, 3, 8, 48, 16
Order of s₀s₁s₂s₃s₄ : 24
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   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 : {3,2,3,12}*576, {3,2,6,6}*576
   4-fold quotients : {3,2,3,6}*288, {3,2,6,3}*288
   8-fold quotients : {3,2,3,3}*144
   24-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := ( 6, 8)( 7, 9)(10,11)(12,20)(13,21)(14,24)(15,25)(16,22)(17,23)(18,27)
(19,26)(28,29)(30,33)(31,32)(36,45)(37,44)(38,49)(39,48)(40,47)(41,46)(42,50)
(43,51)(54,56)(55,57)(58,59)(60,68)(61,69)(62,72)(63,73)(64,70)(65,71)(66,75)
(67,74)(76,77)(78,81)(79,80)(84,93)(85,92)(86,97)(87,96)(88,95)(89,94)(90,98)
(91,99);;
s3 := ( 4,60)( 5,61)( 6,63)( 7,62)( 8,66)( 9,67)(10,64)(11,65)(12,52)(13,53)
(14,55)(15,54)(16,58)(17,59)(18,56)(19,57)(20,68)(21,69)(22,71)(23,70)(24,74)
(25,75)(26,72)(27,73)(28,85)(29,84)(30,86)(31,87)(32,91)(33,90)(34,89)(35,88)
(36,77)(37,76)(38,78)(39,79)(40,83)(41,82)(42,81)(43,80)(44,93)(45,92)(46,94)
(47,95)(48,99)(49,98)(50,97)(51,96);;
s4 := ( 4,34)( 5,35)( 6,31)( 7,30)( 8,32)( 9,33)(10,28)(11,29)(12,50)(13,51)
(14,47)(15,46)(16,48)(17,49)(18,44)(19,45)(20,42)(21,43)(22,39)(23,38)(24,40)
(25,41)(26,36)(27,37)(52,82)(53,83)(54,79)(55,78)(56,80)(57,81)(58,76)(59,77)
(60,98)(61,99)(62,95)(63,94)(64,96)(65,97)(66,92)(67,93)(68,90)(69,91)(70,87)
(71,86)(72,88)(73,89)(74,84)(75,85);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, 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*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3, 
s4*s2*s3*s4*s3*s4*s3*s4*s2*s3*s4*s3*s4*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(99)!(2,3);
s1 := Sym(99)!(1,2);
s2 := Sym(99)!( 6, 8)( 7, 9)(10,11)(12,20)(13,21)(14,24)(15,25)(16,22)(17,23)
(18,27)(19,26)(28,29)(30,33)(31,32)(36,45)(37,44)(38,49)(39,48)(40,47)(41,46)
(42,50)(43,51)(54,56)(55,57)(58,59)(60,68)(61,69)(62,72)(63,73)(64,70)(65,71)
(66,75)(67,74)(76,77)(78,81)(79,80)(84,93)(85,92)(86,97)(87,96)(88,95)(89,94)
(90,98)(91,99);
s3 := Sym(99)!( 4,60)( 5,61)( 6,63)( 7,62)( 8,66)( 9,67)(10,64)(11,65)(12,52)
(13,53)(14,55)(15,54)(16,58)(17,59)(18,56)(19,57)(20,68)(21,69)(22,71)(23,70)
(24,74)(25,75)(26,72)(27,73)(28,85)(29,84)(30,86)(31,87)(32,91)(33,90)(34,89)
(35,88)(36,77)(37,76)(38,78)(39,79)(40,83)(41,82)(42,81)(43,80)(44,93)(45,92)
(46,94)(47,95)(48,99)(49,98)(50,97)(51,96);
s4 := Sym(99)!( 4,34)( 5,35)( 6,31)( 7,30)( 8,32)( 9,33)(10,28)(11,29)(12,50)
(13,51)(14,47)(15,46)(16,48)(17,49)(18,44)(19,45)(20,42)(21,43)(22,39)(23,38)
(24,40)(25,41)(26,36)(27,37)(52,82)(53,83)(54,79)(55,78)(56,80)(57,81)(58,76)
(59,77)(60,98)(61,99)(62,95)(63,94)(64,96)(65,97)(66,92)(67,93)(68,90)(69,91)
(70,87)(71,86)(72,88)(73,89)(74,84)(75,85);
poly := sub<Sym(99)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, 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*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3, 
s4*s2*s3*s4*s3*s4*s3*s4*s2*s3*s4*s3*s4*s3 >;

to this polytope