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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,8,3}*768
if this polytope has a name.
Group : SmallGroup(768,1090163)
Rank : 6
Schlafli Type : {2,2,2,8,3}
Number of vertices, edges, etc : 2, 2, 2, 16, 24, 6
Order of s₀s₁s₂s₃s₄s₅ : 12
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 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 : {2,2,2,4,3}*384
   4-fold quotients : {2,2,2,4,3}*192
   8-fold quotients : {2,2,2,2,3}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := ( 7,17)( 8,13)( 9,12)(10,33)(11,35)(14,18)(15,22)(16,24)(19,21)(20,23)
(25,50)(26,54)(27,49)(28,52)(29,53)(30,51)(31,34)(32,36)(37,45)(38,47)(39,43)
(40,46)(41,48)(42,44);;
s4 := ( 8, 9)(10,11)(12,25)(13,28)(15,20)(16,19)(17,37)(18,40)(21,43)(22,44)
(23,29)(24,26)(27,48)(30,47)(31,32)(33,49)(34,51)(35,38)(36,41)(39,53)(42,54)
(45,46);;
s5 := ( 7,11)( 8,20)( 9,16)(12,24)(13,23)(14,32)(15,19)(17,35)(18,36)(21,22)
(25,27)(26,48)(28,30)(29,47)(37,39)(38,53)(40,42)(41,54)(43,45)(44,46)(49,50)
(51,52);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5*s4*s5, s3*s5*s4*s3*s5*s4*s3*s4*s3*s5*s4*s3*s5*s4*s3*s4, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(54)!(1,2);
s1 := Sym(54)!(3,4);
s2 := Sym(54)!(5,6);
s3 := Sym(54)!( 7,17)( 8,13)( 9,12)(10,33)(11,35)(14,18)(15,22)(16,24)(19,21)
(20,23)(25,50)(26,54)(27,49)(28,52)(29,53)(30,51)(31,34)(32,36)(37,45)(38,47)
(39,43)(40,46)(41,48)(42,44);
s4 := Sym(54)!( 8, 9)(10,11)(12,25)(13,28)(15,20)(16,19)(17,37)(18,40)(21,43)
(22,44)(23,29)(24,26)(27,48)(30,47)(31,32)(33,49)(34,51)(35,38)(36,41)(39,53)
(42,54)(45,46);
s5 := Sym(54)!( 7,11)( 8,20)( 9,16)(12,24)(13,23)(14,32)(15,19)(17,35)(18,36)
(21,22)(25,27)(26,48)(28,30)(29,47)(37,39)(38,53)(40,42)(41,54)(43,45)(44,46)
(49,50)(51,52);
poly := sub<Sym(54)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5*s4*s5, 
s3*s5*s4*s3*s5*s4*s3*s4*s3*s5*s4*s3*s5*s4*s3*s4, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

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