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Polytope of Type {6,8,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,8,2,3}*1152b
if this polytope has a name.
Group : SmallGroup(1152,157603)
Rank : 5
Schlafli Type : {6,8,2,3}
Number of vertices, edges, etc : 12, 48, 16, 3, 3
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 : {3,8,2,3}*576, {6,4,2,3}*576
   4-fold quotients : {3,4,2,3}*288, {6,4,2,3}*288b, {6,4,2,3}*288c
   8-fold quotients : {3,4,2,3}*144, {6,2,2,3}*144
   16-fold quotients : {3,2,2,3}*72
   24-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 5)( 4, 6)( 7, 8)( 9,17)(10,18)(11,21)(12,22)(13,19)(14,20)(15,24)
(16,23)(25,26)(27,30)(28,29)(33,42)(34,41)(35,46)(36,45)(37,44)(38,43)(39,47)
(40,48)(51,53)(52,54)(55,56)(57,65)(58,66)(59,69)(60,70)(61,67)(62,68)(63,72)
(64,71)(73,74)(75,78)(76,77)(81,90)(82,89)(83,94)(84,93)(85,92)(86,91)(87,95)
(88,96);;
s1 := ( 1,57)( 2,58)( 3,60)( 4,59)( 5,63)( 6,64)( 7,61)( 8,62)( 9,49)(10,50)
(11,52)(12,51)(13,55)(14,56)(15,53)(16,54)(17,65)(18,66)(19,68)(20,67)(21,71)
(22,72)(23,69)(24,70)(25,82)(26,81)(27,83)(28,84)(29,88)(30,87)(31,86)(32,85)
(33,74)(34,73)(35,75)(36,76)(37,80)(38,79)(39,78)(40,77)(41,90)(42,89)(43,91)
(44,92)(45,96)(46,95)(47,94)(48,93);;
s2 := ( 1,31)( 2,32)( 3,29)( 4,30)( 5,28)( 6,27)( 7,26)( 8,25)( 9,39)(10,40)
(11,37)(12,38)(13,36)(14,35)(15,34)(16,33)(17,47)(18,48)(19,45)(20,46)(21,44)
(22,43)(23,42)(24,41)(49,79)(50,80)(51,77)(52,78)(53,76)(54,75)(55,74)(56,73)
(57,87)(58,88)(59,85)(60,86)(61,84)(62,83)(63,82)(64,81)(65,95)(66,96)(67,93)
(68,94)(69,92)(70,91)(71,90)(72,89);;
s3 := (98,99);;
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, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(99)!( 3, 5)( 4, 6)( 7, 8)( 9,17)(10,18)(11,21)(12,22)(13,19)(14,20)
(15,24)(16,23)(25,26)(27,30)(28,29)(33,42)(34,41)(35,46)(36,45)(37,44)(38,43)
(39,47)(40,48)(51,53)(52,54)(55,56)(57,65)(58,66)(59,69)(60,70)(61,67)(62,68)
(63,72)(64,71)(73,74)(75,78)(76,77)(81,90)(82,89)(83,94)(84,93)(85,92)(86,91)
(87,95)(88,96);
s1 := Sym(99)!( 1,57)( 2,58)( 3,60)( 4,59)( 5,63)( 6,64)( 7,61)( 8,62)( 9,49)
(10,50)(11,52)(12,51)(13,55)(14,56)(15,53)(16,54)(17,65)(18,66)(19,68)(20,67)
(21,71)(22,72)(23,69)(24,70)(25,82)(26,81)(27,83)(28,84)(29,88)(30,87)(31,86)
(32,85)(33,74)(34,73)(35,75)(36,76)(37,80)(38,79)(39,78)(40,77)(41,90)(42,89)
(43,91)(44,92)(45,96)(46,95)(47,94)(48,93);
s2 := Sym(99)!( 1,31)( 2,32)( 3,29)( 4,30)( 5,28)( 6,27)( 7,26)( 8,25)( 9,39)
(10,40)(11,37)(12,38)(13,36)(14,35)(15,34)(16,33)(17,47)(18,48)(19,45)(20,46)
(21,44)(22,43)(23,42)(24,41)(49,79)(50,80)(51,77)(52,78)(53,76)(54,75)(55,74)
(56,73)(57,87)(58,88)(59,85)(60,86)(61,84)(62,83)(63,82)(64,81)(65,95)(66,96)
(67,93)(68,94)(69,92)(70,91)(71,90)(72,89);
s3 := Sym(99)!(98,99);
s4 := Sym(99)!(97,98);
poly := sub<Sym(99)|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, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1 >; 
 

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