Polytope of Type {8,4,3,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,4,3,2}*768
if this polytope has a name.
Group : SmallGroup(768,1089270)
Rank : 5
Schlafli Type : {8,4,3,2}
Number of vertices, edges, etc : 8, 32, 12, 6, 2
Order of s₀s₁s₂s₃s₄ : 24
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 : {4,4,3,2}*384b
   4-fold quotients : {8,2,3,2}*192, {2,4,3,2}*192
   8-fold quotients : {4,2,3,2}*96, {2,4,3,2}*96
   16-fold quotients : {2,2,3,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope