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

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

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

Permutation Representation (Magma) :

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

to this polytope