Polytope of Type {6,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,24}*1152f
if this polytope has a name.
Group : SmallGroup(1152,155791)
Rank : 3
Schlafli Type : {6,24}
Number of vertices, edges, etc : 24, 288, 96
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 24
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {6,8}*384d
   4-fold quotients : {6,12}*288b
   6-fold quotients : {6,8}*192a
   8-fold quotients : {3,12}*144
   12-fold quotients : {6,4}*96
   16-fold quotients : {6,6}*72c
   24-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
   32-fold quotients : {3,6}*36
   48-fold quotients : {3,4}*24, {6,2}*24
   96-fold quotients : {3,2}*12
   144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 3, 4)( 5, 6)( 9,13)(10,14)(11,16)(12,15)(17,33)(18,34)(19,36)(20,35)
(21,38)(22,37)(23,39)(24,40)(25,45)(26,46)(27,48)(28,47)(29,41)(30,42)(31,44)
(32,43);;
s1 := ( 1,17)( 2,20)( 3,19)( 4,18)( 5,31)( 6,30)( 7,29)( 8,32)( 9,27)(10,26)
(11,25)(12,28)(13,23)(14,22)(15,21)(16,24)(34,36)(37,47)(38,46)(39,45)(40,48)
(41,43);;
s2 := ( 1, 7)( 2, 8)( 3, 5)( 4, 6)( 9,13)(10,14)(11,15)(12,16)(17,39)(18,40)
(19,37)(20,38)(21,35)(22,36)(23,33)(24,34)(25,45)(26,46)(27,47)(28,48)(29,41)
(30,42)(31,43)(32,44);;
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(48)!( 3, 4)( 5, 6)( 9,13)(10,14)(11,16)(12,15)(17,33)(18,34)(19,36)
(20,35)(21,38)(22,37)(23,39)(24,40)(25,45)(26,46)(27,48)(28,47)(29,41)(30,42)
(31,44)(32,43);
s1 := Sym(48)!( 1,17)( 2,20)( 3,19)( 4,18)( 5,31)( 6,30)( 7,29)( 8,32)( 9,27)
(10,26)(11,25)(12,28)(13,23)(14,22)(15,21)(16,24)(34,36)(37,47)(38,46)(39,45)
(40,48)(41,43);
s2 := Sym(48)!( 1, 7)( 2, 8)( 3, 5)( 4, 6)( 9,13)(10,14)(11,15)(12,16)(17,39)
(18,40)(19,37)(20,38)(21,35)(22,36)(23,33)(24,34)(25,45)(26,46)(27,47)(28,48)
(29,41)(30,42)(31,43)(32,44);
poly := sub<Sym(48)|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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1 >;

References : None.
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