Polytope of Type {6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4}*384a
if this polytope has a name.
Group : SmallGroup(384,17948)
Rank : 3
Schlafli Type : {6,4}
Number of vertices, edges, etc : 48, 96, 32
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {6,4,2} of size 768
Vertex Figure Of :
   {2,6,4} of size 768
   {3,6,4} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,4}*192a
   4-fold quotients : {6,4}*96
   8-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
   16-fold quotients : {3,4}*24, {6,2}*24
   32-fold quotients : {3,2}*12
   48-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,8}*768e, {6,8}*768g, {12,4}*768b, {6,4}*768a, {12,4}*768c, {6,8}*768m, {6,8}*768n, {6,4}*768b, {6,4}*768c, {12,4}*768g, {12,4}*768h
   3-fold covers : {18,4}*1152a, {6,12}*1152b, {6,12}*1152c
   5-fold covers : {6,20}*1920a, {30,4}*1920a
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;

References : None.
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