Polytope of Type {2,12,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,6,2}*768b
if this polytope has a name.
Group : SmallGroup(768,1090163)
Rank : 5
Schlafli Type : {2,12,6,2}
Number of vertices, edges, etc : 2, 16, 48, 8, 2
Order of s₀s₁s₂s₃s₄ : 8
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 : {2,12,3,2}*384, {2,6,6,2}*384
   4-fold quotients : {2,3,6,2}*192, {2,6,3,2}*192
   8-fold quotients : {2,3,3,2}*96
   24-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 5, 7)( 6, 8)( 9,10)(11,19)(12,20)(13,23)(14,24)(15,21)(16,22)(17,26)
(18,25)(27,28)(29,32)(30,31)(35,44)(36,43)(37,48)(38,47)(39,46)(40,45)(41,49)
(42,50)(53,55)(54,56)(57,58)(59,67)(60,68)(61,71)(62,72)(63,69)(64,70)(65,74)
(66,73)(75,76)(77,80)(78,79)(83,92)(84,91)(85,96)(86,95)(87,94)(88,93)(89,97)
(90,98);;
s2 := ( 3,35)( 4,36)( 5,38)( 6,37)( 7,41)( 8,42)( 9,39)(10,40)(11,27)(12,28)
(13,30)(14,29)(15,33)(16,34)(17,31)(18,32)(19,43)(20,44)(21,46)(22,45)(23,49)
(24,50)(25,47)(26,48)(51,83)(52,84)(53,86)(54,85)(55,89)(56,90)(57,87)(58,88)
(59,75)(60,76)(61,78)(62,77)(63,81)(64,82)(65,79)(66,80)(67,91)(68,92)(69,94)
(70,93)(71,97)(72,98)(73,95)(74,96);;
s3 := ( 3,81)( 4,82)( 5,78)( 6,77)( 7,79)( 8,80)( 9,75)(10,76)(11,97)(12,98)
(13,94)(14,93)(15,95)(16,96)(17,91)(18,92)(19,89)(20,90)(21,86)(22,85)(23,87)
(24,88)(25,83)(26,84)(27,57)(28,58)(29,54)(30,53)(31,55)(32,56)(33,51)(34,52)
(35,73)(36,74)(37,70)(38,69)(39,71)(40,72)(41,67)(42,68)(43,65)(44,66)(45,62)
(46,61)(47,63)(48,64)(49,59)(50,60);;
s4 := ( 99,100);;
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*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(100)!(1,2);
s1 := Sym(100)!( 5, 7)( 6, 8)( 9,10)(11,19)(12,20)(13,23)(14,24)(15,21)(16,22)
(17,26)(18,25)(27,28)(29,32)(30,31)(35,44)(36,43)(37,48)(38,47)(39,46)(40,45)
(41,49)(42,50)(53,55)(54,56)(57,58)(59,67)(60,68)(61,71)(62,72)(63,69)(64,70)
(65,74)(66,73)(75,76)(77,80)(78,79)(83,92)(84,91)(85,96)(86,95)(87,94)(88,93)
(89,97)(90,98);
s2 := Sym(100)!( 3,35)( 4,36)( 5,38)( 6,37)( 7,41)( 8,42)( 9,39)(10,40)(11,27)
(12,28)(13,30)(14,29)(15,33)(16,34)(17,31)(18,32)(19,43)(20,44)(21,46)(22,45)
(23,49)(24,50)(25,47)(26,48)(51,83)(52,84)(53,86)(54,85)(55,89)(56,90)(57,87)
(58,88)(59,75)(60,76)(61,78)(62,77)(63,81)(64,82)(65,79)(66,80)(67,91)(68,92)
(69,94)(70,93)(71,97)(72,98)(73,95)(74,96);
s3 := Sym(100)!( 3,81)( 4,82)( 5,78)( 6,77)( 7,79)( 8,80)( 9,75)(10,76)(11,97)
(12,98)(13,94)(14,93)(15,95)(16,96)(17,91)(18,92)(19,89)(20,90)(21,86)(22,85)
(23,87)(24,88)(25,83)(26,84)(27,57)(28,58)(29,54)(30,53)(31,55)(32,56)(33,51)
(34,52)(35,73)(36,74)(37,70)(38,69)(39,71)(40,72)(41,67)(42,68)(43,65)(44,66)
(45,62)(46,61)(47,63)(48,64)(49,59)(50,60);
s4 := Sym(100)!( 99,100);
poly := sub<Sym(100)|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*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2 >;

to this polytope