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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,12,6}*1152b
if this polytope has a name.
Group : SmallGroup(1152,157603)
Rank : 5
Schlafli Type : {3,2,12,6}
Number of vertices, edges, etc : 3, 3, 16, 48, 8
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 : {3,2,12,3}*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 := ( 4,36)( 5,37)( 6,39)( 7,38)( 8,42)( 9,43)(10,40)(11,41)(12,28)(13,29)
(14,31)(15,30)(16,34)(17,35)(18,32)(19,33)(20,44)(21,45)(22,47)(23,46)(24,50)
(25,51)(26,48)(27,49)(52,84)(53,85)(54,87)(55,86)(56,90)(57,91)(58,88)(59,89)
(60,76)(61,77)(62,79)(63,78)(64,82)(65,83)(66,80)(67,81)(68,92)(69,93)(70,95)
(71,94)(72,98)(73,99)(74,96)(75,97);;
s4 := ( 4,82)( 5,83)( 6,79)( 7,78)( 8,80)( 9,81)(10,76)(11,77)(12,98)(13,99)
(14,95)(15,94)(16,96)(17,97)(18,92)(19,93)(20,90)(21,91)(22,87)(23,86)(24,88)
(25,89)(26,84)(27,85)(28,58)(29,59)(30,55)(31,54)(32,56)(33,57)(34,52)(35,53)
(36,74)(37,75)(38,71)(39,70)(40,72)(41,73)(42,68)(43,69)(44,66)(45,67)(46,63)
(47,62)(48,64)(49,65)(50,60)(51,61);;
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*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s4*s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*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)!( 4,36)( 5,37)( 6,39)( 7,38)( 8,42)( 9,43)(10,40)(11,41)(12,28)
(13,29)(14,31)(15,30)(16,34)(17,35)(18,32)(19,33)(20,44)(21,45)(22,47)(23,46)
(24,50)(25,51)(26,48)(27,49)(52,84)(53,85)(54,87)(55,86)(56,90)(57,91)(58,88)
(59,89)(60,76)(61,77)(62,79)(63,78)(64,82)(65,83)(66,80)(67,81)(68,92)(69,93)
(70,95)(71,94)(72,98)(73,99)(74,96)(75,97);
s4 := Sym(99)!( 4,82)( 5,83)( 6,79)( 7,78)( 8,80)( 9,81)(10,76)(11,77)(12,98)
(13,99)(14,95)(15,94)(16,96)(17,97)(18,92)(19,93)(20,90)(21,91)(22,87)(23,86)
(24,88)(25,89)(26,84)(27,85)(28,58)(29,59)(30,55)(31,54)(32,56)(33,57)(34,52)
(35,53)(36,74)(37,75)(38,71)(39,70)(40,72)(41,73)(42,68)(43,69)(44,66)(45,67)
(46,63)(47,62)(48,64)(49,65)(50,60)(51,61);
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*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s4*s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3 >;

to this polytope