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

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

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

Permutation Representation (Magma) :

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

to this polytope