Polytope of Type {4,2,8,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,8,3}*768
if this polytope has a name.
Group : SmallGroup(768,1089307)
Rank : 5
Schlafli Type : {4,2,8,3}
Number of vertices, edges, etc : 4, 4, 16, 24, 6
Order of s₀s₁s₂s₃s₄ : 12
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 : {4,2,4,3}*384, {2,2,8,3}*384
   4-fold quotients : {4,2,4,3}*192, {2,2,4,3}*192
   8-fold quotients : {4,2,2,3}*96, {2,2,4,3}*96
   16-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

to this polytope