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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,8,6,2}*1152
if this polytope has a name.
Group : SmallGroup(1152,152548)
Rank : 5
Schlafli Type : {6,8,6,2}
Number of vertices, edges, etc : 6, 24, 24, 6, 2
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 : {6,4,6,2}*576
   3-fold quotients : {2,8,6,2}*384, {6,8,2,2}*384
   4-fold quotients : {6,2,6,2}*288
   6-fold quotients : {2,4,6,2}*192a, {6,4,2,2}*192a
   8-fold quotients : {3,2,6,2}*144, {6,2,3,2}*144
   9-fold quotients : {2,8,2,2}*128
   12-fold quotients : {2,2,6,2}*96, {6,2,2,2}*96
   16-fold quotients : {3,2,3,2}*72
   18-fold quotients : {2,4,2,2}*64
   24-fold quotients : {2,2,3,2}*48, {3,2,2,2}*48
   36-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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