Polytope of Type {24,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,6}*288a
Also Known As : {24,6|2}. if this polytope has another 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 : 2
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
   {24,6,3} of size 1152
   {24,6,4} of size 1152
   {24,6,6} of size 1728
   {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
   {6,24,6} of size 1728
   {3,24,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,6}*144a
   3-fold quotients : {24,2}*96, {8,6}*96
   4-fold quotients : {6,6}*72a
   6-fold quotients : {12,2}*48, {4,6}*48a
   9-fold quotients : {8,2}*32
   12-fold quotients : {2,6}*24, {6,2}*24
   18-fold quotients : {4,2}*16
   24-fold quotients : {2,3}*12, {3,2}*12
   36-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {48,6}*576a, {24,12}*576c
   3-fold covers : {72,6}*864a, {24,18}*864a, {24,6}*864b, {24,6}*864f
   4-fold covers : {24,12}*1152b, {24,24}*1152b, {24,24}*1152g, {48,12}*1152b, {48,12}*1152e, {96,6}*1152c, {24,12}*1152o, {24,6}*1152h
   5-fold covers : {24,30}*1440b, {120,6}*1440b
   6-fold covers : {144,6}*1728a, {48,18}*1728a, {48,6}*1728b, {72,12}*1728a, {24,36}*1728c, {24,12}*1728d, {48,6}*1728f, {24,12}*1728o
Permutation Representation (GAP) :

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