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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,4,3}*576
if this polytope has a name.
Group : SmallGroup(576,8659)
Rank : 5
Schlafli Type : {2,6,4,3}
Number of vertices, edges, etc : 2, 6, 24, 12, 6
Order of s₀s₁s₂s₃s₄ : 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,4,3,2} of size 1152
Vertex Figure Of :
   {2,2,6,4,3} of size 1152
   {3,2,6,4,3} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,2,4,3}*192
   4-fold quotients : {2,6,2,3}*144
   6-fold quotients : {2,2,4,3}*96
   8-fold quotients : {2,3,2,3}*72
   12-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,12,4,3}*1152, {4,6,4,3}*1152a, {2,6,8,3}*1152, {2,6,4,6}*1152a
   3-fold covers : {2,18,4,3}*1728, {2,6,4,9}*1728, {2,6,12,3}*1728a, {6,6,4,3}*1728a, {6,6,4,3}*1728b, {2,6,12,3}*1728b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope