Polytope of Type {2,4,3,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,3,6}*576
if this polytope has a name.
Group : SmallGroup(576,8659)
Rank : 5
Schlafli Type : {2,4,3,6}
Number of vertices, edges, etc : 2, 8, 12, 18, 6
Order of s₀s₁s₂s₃s₄ : 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,3,6,2} of size 1152
   {2,4,3,6,3} of size 1728
Vertex Figure Of :
   {2,2,4,3,6} of size 1152
   {3,2,4,3,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,4,3,6}*288
   3-fold quotients : {2,4,3,2}*192
   4-fold quotients : {2,2,3,6}*144
   6-fold quotients : {2,4,3,2}*96
   12-fold quotients : {2,2,3,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,4,3,6}*1152b, {2,8,3,6}*1152, {2,4,6,6}*1152b
   3-fold covers : {2,4,9,6}*1728, {2,4,3,6}*1728, {6,4,3,6}*1728, {2,12,3,6}*1728
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 3,40)( 4,39)( 5,42)( 6,41)( 7,44)( 8,43)( 9,46)(10,45)(11,48)(12,47)
(13,50)(14,49)(15,52)(16,51)(17,54)(18,53)(19,56)(20,55)(21,58)(22,57)(23,60)
(24,59)(25,62)(26,61)(27,64)(28,63)(29,66)(30,65)(31,68)(32,67)(33,70)(34,69)
(35,72)(36,71)(37,74)(38,73);;
s2 := ( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(15,27)(16,29)(17,28)(18,30)(19,35)
(20,37)(21,36)(22,38)(23,31)(24,33)(25,32)(26,34)(40,41)(43,47)(44,49)(45,48)
(46,50)(51,63)(52,65)(53,64)(54,66)(55,71)(56,73)(57,72)(58,74)(59,67)(60,69)
(61,68)(62,70);;
s3 := ( 3,19)( 4,20)( 5,22)( 6,21)( 7,15)( 8,16)( 9,18)(10,17)(11,23)(12,24)
(13,26)(14,25)(27,31)(28,32)(29,34)(30,33)(37,38)(39,55)(40,56)(41,58)(42,57)
(43,51)(44,52)(45,54)(46,53)(47,59)(48,60)(49,62)(50,61)(63,67)(64,68)(65,70)
(66,69)(73,74);;
s4 := ( 7,11)( 8,12)( 9,13)(10,14)(19,23)(20,24)(21,25)(22,26)(31,35)(32,36)
(33,37)(34,38)(43,47)(44,48)(45,49)(46,50)(55,59)(56,60)(57,61)(58,62)(67,71)
(68,72)(69,73)(70,74);;
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, 
s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(74)!(1,2);
s1 := Sym(74)!( 3,40)( 4,39)( 5,42)( 6,41)( 7,44)( 8,43)( 9,46)(10,45)(11,48)
(12,47)(13,50)(14,49)(15,52)(16,51)(17,54)(18,53)(19,56)(20,55)(21,58)(22,57)
(23,60)(24,59)(25,62)(26,61)(27,64)(28,63)(29,66)(30,65)(31,68)(32,67)(33,70)
(34,69)(35,72)(36,71)(37,74)(38,73);
s2 := Sym(74)!( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(15,27)(16,29)(17,28)(18,30)
(19,35)(20,37)(21,36)(22,38)(23,31)(24,33)(25,32)(26,34)(40,41)(43,47)(44,49)
(45,48)(46,50)(51,63)(52,65)(53,64)(54,66)(55,71)(56,73)(57,72)(58,74)(59,67)
(60,69)(61,68)(62,70);
s3 := Sym(74)!( 3,19)( 4,20)( 5,22)( 6,21)( 7,15)( 8,16)( 9,18)(10,17)(11,23)
(12,24)(13,26)(14,25)(27,31)(28,32)(29,34)(30,33)(37,38)(39,55)(40,56)(41,58)
(42,57)(43,51)(44,52)(45,54)(46,53)(47,59)(48,60)(49,62)(50,61)(63,67)(64,68)
(65,70)(66,69)(73,74);
s4 := Sym(74)!( 7,11)( 8,12)( 9,13)(10,14)(19,23)(20,24)(21,25)(22,26)(31,35)
(32,36)(33,37)(34,38)(43,47)(44,48)(45,49)(46,50)(55,59)(56,60)(57,61)(58,62)
(67,71)(68,72)(69,73)(70,74);
poly := sub<Sym(74)|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, s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3 >;

to this polytope