Polytope of Type {8,4,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,4,6}*576
if this polytope has a name.
Group : SmallGroup(576,5339)
Rank : 4
Schlafli Type : {8,4,6}
Number of vertices, edges, etc : 8, 24, 18, 9
Order of s₀s₁s₂s₃ : 8
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,4,6,2} of size 1152
Vertex Figure Of :
   {2,8,4,6} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,4,6}*288
   4-fold quotients : {2,4,6}*144
Covers (Minimal Covers in Boldface) :
   2-fold covers : {16,4,6}*1152, {8,4,6}*1152a
   3-fold covers : {8,4,6}*1728, {8,12,6}*1728a, {8,12,6}*1728b, {24,4,6}*1728, {8,12,6}*1728c
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope