Polytope of Type {12,3,4,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,3,4,2}*1152
if this polytope has a name.
Group : SmallGroup(1152,157864)
Rank : 5
Schlafli Type : {12,3,4,2}
Number of vertices, edges, etc : 24, 36, 12, 4, 2
Order of s₀s₁s₂s₃s₄ : 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   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 : {4,3,4,2}*384b
   4-fold quotients : {6,3,4,2}*288
   6-fold quotients : {4,3,4,2}*192
   12-fold quotients : {2,3,4,2}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 1, 9)( 2,10)( 3,11)( 4,12)( 5,13)( 6,14)( 7,15)( 8,16)(17,41)(18,42)
(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)(25,33)(26,34)(27,35)(28,36)(29,37)
(30,38)(31,39)(32,40);;
s1 := ( 1,17)( 2,19)( 3,18)( 4,20)( 5,25)( 6,27)( 7,26)( 8,28)( 9,21)(10,23)
(11,22)(12,24)(13,29)(14,31)(15,30)(16,32)(34,35)(37,41)(38,43)(39,42)(40,44)
(46,47);;
s2 := ( 3, 4)( 5,13)( 6,14)( 7,16)( 8,15)(11,12)(17,33)(18,34)(19,36)(20,35)
(21,45)(22,46)(23,48)(24,47)(25,41)(26,42)(27,44)(28,43)(29,37)(30,38)(31,40)
(32,39);;
s3 := ( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,20)(18,19)
(21,24)(22,23)(25,28)(26,27)(29,32)(30,31)(33,36)(34,35)(37,40)(38,39)(41,44)
(42,43)(45,48)(46,47);;
s4 := (49,50);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s3*s2*s1*s3*s2*s1*s3*s2, s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(50)!( 1, 9)( 2,10)( 3,11)( 4,12)( 5,13)( 6,14)( 7,15)( 8,16)(17,41)
(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)(25,33)(26,34)(27,35)(28,36)
(29,37)(30,38)(31,39)(32,40);
s1 := Sym(50)!( 1,17)( 2,19)( 3,18)( 4,20)( 5,25)( 6,27)( 7,26)( 8,28)( 9,21)
(10,23)(11,22)(12,24)(13,29)(14,31)(15,30)(16,32)(34,35)(37,41)(38,43)(39,42)
(40,44)(46,47);
s2 := Sym(50)!( 3, 4)( 5,13)( 6,14)( 7,16)( 8,15)(11,12)(17,33)(18,34)(19,36)
(20,35)(21,45)(22,46)(23,48)(24,47)(25,41)(26,42)(27,44)(28,43)(29,37)(30,38)
(31,40)(32,39);
s3 := Sym(50)!( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,20)
(18,19)(21,24)(22,23)(25,28)(26,27)(29,32)(30,31)(33,36)(34,35)(37,40)(38,39)
(41,44)(42,43)(45,48)(46,47);
s4 := Sym(50)!(49,50);
poly := sub<Sym(50)|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, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s3*s2*s1*s3*s2*s1*s3*s2, 
s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1 >;

to this polytope