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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,3,8}*576
if this polytope has a name.
Group : SmallGroup(576,8340)
Rank : 5
Schlafli Type : {3,2,3,8}
Number of vertices, edges, etc : 3, 3, 6, 24, 16
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,3,8,2} of size 1152
Vertex Figure Of :
   {2,3,2,3,8} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,3,4}*288
   4-fold quotients : {3,2,3,4}*144
   8-fold quotients : {3,2,3,2}*72
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,6,8}*1152b, {6,2,3,8}*1152
   3-fold covers : {9,2,3,8}*1728, {3,2,9,8}*1728, {3,6,3,8}*1728, {3,2,3,24}*1728
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope