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Polytope of Type {9,4,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,4,2}*288
if this polytope has a name.
Group : SmallGroup(288,835)
Rank : 4
Schlafli Type : {9,4,2}
Number of vertices, edges, etc : 18, 36, 8, 2
Order of s0s1s2s3 : 18
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {9,4,2,2} of size 576
   {9,4,2,3} of size 864
   {9,4,2,4} of size 1152
   {9,4,2,5} of size 1440
   {9,4,2,6} of size 1728
Vertex Figure Of :
   {2,9,4,2} of size 576
   {4,9,4,2} of size 1152
   {6,9,4,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {9,4,2}*144
   3-fold quotients : {3,4,2}*96
   4-fold quotients : {9,2,2}*72
   6-fold quotients : {3,4,2}*48
   12-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {9,4,4}*576b, {9,8,2}*576, {18,4,2}*576
   3-fold covers : {27,4,2}*864, {9,4,6}*864, {9,12,2}*864
   4-fold covers : {9,4,4}*1152b, {9,8,2}*1152, {9,8,4}*1152, {9,4,8}*1152, {36,4,2}*1152b, {18,4,4}*1152d, {18,4,2}*1152b, {36,4,2}*1152c, {18,8,2}*1152b, {18,8,2}*1152c
   5-fold covers : {9,4,10}*1440, {45,4,2}*1440
   6-fold covers : {27,4,4}*1728b, {27,8,2}*1728, {54,4,2}*1728, {9,4,12}*1728, {9,24,2}*1728, {9,8,6}*1728, {9,12,4}*1728, {18,4,6}*1728b, {18,12,2}*1728a, {18,12,2}*1728b
Permutation Representation (GAP) :
s0 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(13,29)(14,31)(15,30)(16,32)(17,25)
(18,27)(19,26)(20,28)(21,33)(22,35)(23,34)(24,36)(38,39)(41,45)(42,47)(43,46)
(44,48)(49,65)(50,67)(51,66)(52,68)(53,61)(54,63)(55,62)(56,64)(57,69)(58,71)
(59,70)(60,72);;
s1 := ( 1,13)( 2,14)( 3,16)( 4,15)( 5,21)( 6,22)( 7,24)( 8,23)( 9,17)(10,18)
(11,20)(12,19)(25,29)(26,30)(27,32)(28,31)(35,36)(37,49)(38,50)(39,52)(40,51)
(41,57)(42,58)(43,60)(44,59)(45,53)(46,54)(47,56)(48,55)(61,65)(62,66)(63,68)
(64,67)(71,72);;
s2 := ( 1,40)( 2,39)( 3,38)( 4,37)( 5,44)( 6,43)( 7,42)( 8,41)( 9,48)(10,47)
(11,46)(12,45)(13,52)(14,51)(15,50)(16,49)(17,56)(18,55)(19,54)(20,53)(21,60)
(22,59)(23,58)(24,57)(25,64)(26,63)(27,62)(28,61)(29,68)(30,67)(31,66)(32,65)
(33,72)(34,71)(35,70)(36,69);;
s3 := (73,74);;
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, s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2, 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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(74)!( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(13,29)(14,31)(15,30)(16,32)
(17,25)(18,27)(19,26)(20,28)(21,33)(22,35)(23,34)(24,36)(38,39)(41,45)(42,47)
(43,46)(44,48)(49,65)(50,67)(51,66)(52,68)(53,61)(54,63)(55,62)(56,64)(57,69)
(58,71)(59,70)(60,72);
s1 := Sym(74)!( 1,13)( 2,14)( 3,16)( 4,15)( 5,21)( 6,22)( 7,24)( 8,23)( 9,17)
(10,18)(11,20)(12,19)(25,29)(26,30)(27,32)(28,31)(35,36)(37,49)(38,50)(39,52)
(40,51)(41,57)(42,58)(43,60)(44,59)(45,53)(46,54)(47,56)(48,55)(61,65)(62,66)
(63,68)(64,67)(71,72);
s2 := Sym(74)!( 1,40)( 2,39)( 3,38)( 4,37)( 5,44)( 6,43)( 7,42)( 8,41)( 9,48)
(10,47)(11,46)(12,45)(13,52)(14,51)(15,50)(16,49)(17,56)(18,55)(19,54)(20,53)
(21,60)(22,59)(23,58)(24,57)(25,64)(26,63)(27,62)(28,61)(29,68)(30,67)(31,66)
(32,65)(33,72)(34,71)(35,70)(36,69);
s3 := Sym(74)!(73,74);
poly := sub<Sym(74)|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, 
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2, 
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 >; 
 

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