Polytope of Type {6,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,24}*288c
if this polytope has a name.
Group : SmallGroup(288,574)
Rank : 3
Schlafli Type : {6,24}
Number of vertices, edges, etc : 6, 72, 24
Order of s₀s₁s₂ : 24
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,24,2} of size 576
   {6,24,4} of size 1152
   {6,24,4} of size 1152
   {6,24,6} of size 1728
   {6,24,3} of size 1728
   {6,24,6} of size 1728
Vertex Figure Of :
   {2,6,24} of size 576
   {4,6,24} of size 1152
   {4,6,24} of size 1152
   {6,6,24} of size 1728
   {6,6,24} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,12}*144c
   3-fold quotients : {6,8}*96
   4-fold quotients : {6,6}*72c
   6-fold quotients : {6,4}*48a
   8-fold quotients : {3,6}*36
   9-fold quotients : {2,8}*32
   12-fold quotients : {6,2}*24
   18-fold quotients : {2,4}*16
   24-fold quotients : {3,2}*12
   36-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,24}*576b, {6,48}*576c
   3-fold covers : {18,24}*864b, {6,24}*864c, {6,24}*864f
   4-fold covers : {12,24}*1152c, {24,24}*1152d, {24,24}*1152e, {12,48}*1152c, {12,48}*1152f, {6,96}*1152a, {6,24}*1152j, {6,24}*1152k
   5-fold covers : {6,120}*1440a, {30,24}*1440c
   6-fold covers : {36,24}*1728b, {12,24}*1728b, {18,48}*1728b, {6,48}*1728c, {6,48}*1728f, {12,24}*1728o
Permutation Representation (GAP) :

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

References : None.
to this polytope