Polytope of Type {24,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,6}*288b
if this polytope has a name.
Group : SmallGroup(288,441)
Rank : 3
Schlafli Type : {24,6}
Number of vertices, edges, etc : 24, 72, 6
Order of s₀s₁s₂ : 24
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {24,6,2} of size 576
   {24,6,3} of size 864
   {24,6,4} of size 1152
   {24,6,6} of size 1728
   {24,6,6} of size 1728
Vertex Figure Of :
   {2,24,6} of size 576
   {4,24,6} of size 1152
   {4,24,6} of size 1152
   {4,24,6} of size 1152
   {4,24,6} of size 1152
   {6,24,6} of size 1728
   {6,24,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,6}*144b
   3-fold quotients : {24,2}*96
   4-fold quotients : {6,6}*72c
   6-fold quotients : {12,2}*48
   8-fold quotients : {3,6}*36
   9-fold quotients : {8,2}*32
   12-fold quotients : {6,2}*24
   18-fold quotients : {4,2}*16
   24-fold quotients : {3,2}*12
   36-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {48,6}*576b, {24,12}*576d
   3-fold covers : {72,6}*864b, {24,6}*864a, {24,6}*864f
   4-fold covers : {24,12}*1152a, {24,24}*1152c, {24,24}*1152e, {48,12}*1152a, {48,12}*1152d, {96,6}*1152b, {24,12}*1152p, {24,6}*1152g
   5-fold covers : {24,30}*1440a, {120,6}*1440c
   6-fold covers : {144,6}*1728b, {48,6}*1728a, {72,12}*1728b, {24,12}*1728c, {48,6}*1728f, {24,12}*1728o
Permutation Representation (GAP) :

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

References : None.
to this polytope