Polytope of Type {2,6,8,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,8,2}*768b
if this polytope has a name.
Group : SmallGroup(768,1090163)
Rank : 5
Schlafli Type : {2,6,8,2}
Number of vertices, edges, etc : 2, 12, 48, 16, 2
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 : {2,3,8,2}*384, {2,6,4,2}*384
   4-fold quotients : {2,3,4,2}*192, {2,6,4,2}*192b, {2,6,4,2}*192c
   8-fold quotients : {2,3,4,2}*96, {2,6,2,2}*96
   16-fold quotients : {2,3,2,2}*48
   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 := ( 3,59)( 4,60)( 5,62)( 6,61)( 7,65)( 8,66)( 9,63)(10,64)(11,51)(12,52)
(13,54)(14,53)(15,57)(16,58)(17,55)(18,56)(19,67)(20,68)(21,70)(22,69)(23,73)
(24,74)(25,71)(26,72)(27,84)(28,83)(29,85)(30,86)(31,90)(32,89)(33,88)(34,87)
(35,76)(36,75)(37,77)(38,78)(39,82)(40,81)(41,80)(42,79)(43,92)(44,91)(45,93)
(46,94)(47,98)(48,97)(49,96)(50,95);;
s3 := ( 3,33)( 4,34)( 5,31)( 6,32)( 7,30)( 8,29)( 9,28)(10,27)(11,41)(12,42)
(13,39)(14,40)(15,38)(16,37)(17,36)(18,35)(19,49)(20,50)(21,47)(22,48)(23,46)
(24,45)(25,44)(26,43)(51,81)(52,82)(53,79)(54,80)(55,78)(56,77)(57,76)(58,75)
(59,89)(60,90)(61,87)(62,88)(63,86)(64,85)(65,84)(66,83)(67,97)(68,98)(69,95)
(70,96)(71,94)(72,93)(73,92)(74,91);;
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*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(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)!( 3,59)( 4,60)( 5,62)( 6,61)( 7,65)( 8,66)( 9,63)(10,64)(11,51)
(12,52)(13,54)(14,53)(15,57)(16,58)(17,55)(18,56)(19,67)(20,68)(21,70)(22,69)
(23,73)(24,74)(25,71)(26,72)(27,84)(28,83)(29,85)(30,86)(31,90)(32,89)(33,88)
(34,87)(35,76)(36,75)(37,77)(38,78)(39,82)(40,81)(41,80)(42,79)(43,92)(44,91)
(45,93)(46,94)(47,98)(48,97)(49,96)(50,95);
s3 := Sym(100)!( 3,33)( 4,34)( 5,31)( 6,32)( 7,30)( 8,29)( 9,28)(10,27)(11,41)
(12,42)(13,39)(14,40)(15,38)(16,37)(17,36)(18,35)(19,49)(20,50)(21,47)(22,48)
(23,46)(24,45)(25,44)(26,43)(51,81)(52,82)(53,79)(54,80)(55,78)(56,77)(57,76)
(58,75)(59,89)(60,90)(61,87)(62,88)(63,86)(64,85)(65,84)(66,83)(67,97)(68,98)
(69,95)(70,96)(71,94)(72,93)(73,92)(74,91);
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2 >;

to this polytope