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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,12,4}*768b
if this polytope has a name.
Group : SmallGroup(768,1088766)
Rank : 5
Schlafli Type : {4,2,12,4}
Number of vertices, edges, etc : 4, 4, 12, 24, 4
Order of s₀s₁s₂s₃s₄ : 12
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) :
   2-fold quotients : {2,2,12,4}*384b, {4,2,6,4}*384c
   4-fold quotients : {4,2,3,4}*192, {2,2,6,4}*192c
   8-fold quotients : {2,2,3,4}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 6, 7)( 8, 9)(10,20)(12,16)(13,15)(14,28)(17,33)(18,36)(19,21)(22,38)
(23,24)(25,41)(26,44)(27,34)(29,32)(30,48)(31,45)(35,47)(39,50)(40,42)(43,52)
(46,49);;
s3 := ( 5,12)( 6, 8)( 7,23)( 9,13)(10,47)(11,15)(14,38)(16,24)(17,52)(18,46)
(19,30)(20,29)(21,33)(22,27)(25,48)(26,37)(28,42)(31,51)(32,43)(34,41)(35,40)
(36,45)(39,49)(44,50);;
s4 := ( 5,37)( 6,46)( 7,49)( 8,38)( 9,22)(10,20)(11,51)(12,47)(13,30)(14,33)
(15,48)(16,35)(17,28)(18,21)(19,36)(23,52)(24,43)(25,41)(26,29)(27,45)(31,34)
(32,44)(39,42)(40,50);;
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, 
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*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4, 
s4*s3*s2*s4*s3*s4*s3*s2*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(52)!(2,3);
s1 := Sym(52)!(1,2)(3,4);
s2 := Sym(52)!( 6, 7)( 8, 9)(10,20)(12,16)(13,15)(14,28)(17,33)(18,36)(19,21)
(22,38)(23,24)(25,41)(26,44)(27,34)(29,32)(30,48)(31,45)(35,47)(39,50)(40,42)
(43,52)(46,49);
s3 := Sym(52)!( 5,12)( 6, 8)( 7,23)( 9,13)(10,47)(11,15)(14,38)(16,24)(17,52)
(18,46)(19,30)(20,29)(21,33)(22,27)(25,48)(26,37)(28,42)(31,51)(32,43)(34,41)
(35,40)(36,45)(39,49)(44,50);
s4 := Sym(52)!( 5,37)( 6,46)( 7,49)( 8,38)( 9,22)(10,20)(11,51)(12,47)(13,30)
(14,33)(15,48)(16,35)(17,28)(18,21)(19,36)(23,52)(24,43)(25,41)(26,29)(27,45)
(31,34)(32,44)(39,42)(40,50);
poly := sub<Sym(52)|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*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4, s4*s3*s2*s4*s3*s4*s3*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope