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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,12,4}*384c
if this polytope has a name.
Group : SmallGroup(384,20049)
Rank : 5
Schlafli Type : {2,2,12,4}
Number of vertices, edges, etc : 2, 2, 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 :
   {2,2,12,4,2} of size 768
Vertex Figure Of :
   {2,2,2,12,4} of size 768
   {3,2,2,12,4} of size 1152
   {5,2,2,12,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,6,4}*192c
   4-fold quotients : {2,2,3,4}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,12,4}*768c, {4,2,12,4}*768c, {2,2,12,4}*768b
   3-fold covers : {2,2,36,4}*1152c, {2,6,12,4}*1152e, {2,6,12,4}*1152g, {6,2,12,4}*1152c
   5-fold covers : {2,10,12,4}*1920c, {10,2,12,4}*1920c, {2,2,60,4}*1920c
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope