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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,8,2}*384
if this polytope has a name.
Group : SmallGroup(384,20062)
Rank : 5
Schlafli Type : {2,3,8,2}
Number of vertices, edges, etc : 2, 6, 24, 16, 2
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,3,8,2,2} of size 768
   {2,3,8,2,3} of size 1152
   {2,3,8,2,5} of size 1920
Vertex Figure Of :
   {2,2,3,8,2} of size 768
   {3,2,3,8,2} of size 1152
   {5,2,3,8,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,3,4,2}*192
   4-fold quotients : {2,3,4,2}*96
   8-fold quotients : {2,3,2,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,3,8,4}*768, {2,6,8,2}*768b
   3-fold covers : {2,9,8,2}*1152, {2,3,24,2}*1152, {2,3,8,6}*1152, {6,3,8,2}*1152
   5-fold covers : {2,3,8,10}*1920, {2,15,8,2}*1920
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope