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Polytope of Type {18,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,6,2}*432a
if this polytope has a name.
Group : SmallGroup(432,544)
Rank : 4
Schlafli Type : {18,6,2}
Number of vertices, edges, etc : 18, 54, 6, 2
Order of s0s1s2s3 : 18
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {18,6,2,2} of size 864
   {18,6,2,3} of size 1296
   {18,6,2,4} of size 1728
Vertex Figure Of :
   {2,18,6,2} of size 864
   {4,18,6,2} of size 1728
   {4,18,6,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {18,2,2}*144, {6,6,2}*144a
   6-fold quotients : {9,2,2}*72
   9-fold quotients : {2,6,2}*48, {6,2,2}*48
   18-fold quotients : {2,3,2}*24, {3,2,2}*24
   27-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {36,6,2}*864a, {18,12,2}*864a, {18,6,4}*864a
   3-fold covers : {18,18,2}*1296a, {18,6,2}*1296b, {54,6,2}*1296a, {18,6,6}*1296b, {18,6,6}*1296d, {18,6,2}*1296i
   4-fold covers : {36,6,4}*1728a, {18,12,4}*1728a, {72,6,2}*1728a, {18,24,2}*1728a, {18,6,8}*1728a, {36,12,2}*1728a, {18,6,4}*1728, {36,6,2}*1728, {18,12,2}*1728a
Permutation Representation (GAP) :
s0 := ( 2, 3)( 5, 6)( 8, 9)(10,20)(11,19)(12,21)(13,23)(14,22)(15,24)(16,26)
(17,25)(18,27)(29,30)(32,33)(35,36)(37,47)(38,46)(39,48)(40,50)(41,49)(42,51)
(43,53)(44,52)(45,54);;
s1 := ( 1,10)( 2,12)( 3,11)( 4,16)( 5,18)( 6,17)( 7,13)( 8,15)( 9,14)(19,20)
(22,26)(23,25)(24,27)(28,37)(29,39)(30,38)(31,43)(32,45)(33,44)(34,40)(35,42)
(36,41)(46,47)(49,53)(50,52)(51,54);;
s2 := ( 1,31)( 2,32)( 3,33)( 4,28)( 5,29)( 6,30)( 7,34)( 8,35)( 9,36)(10,40)
(11,41)(12,42)(13,37)(14,38)(15,39)(16,43)(17,44)(18,45)(19,49)(20,50)(21,51)
(22,46)(23,47)(24,48)(25,52)(26,53)(27,54);;
s3 := (55,56);;
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, 
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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(56)!( 2, 3)( 5, 6)( 8, 9)(10,20)(11,19)(12,21)(13,23)(14,22)(15,24)
(16,26)(17,25)(18,27)(29,30)(32,33)(35,36)(37,47)(38,46)(39,48)(40,50)(41,49)
(42,51)(43,53)(44,52)(45,54);
s1 := Sym(56)!( 1,10)( 2,12)( 3,11)( 4,16)( 5,18)( 6,17)( 7,13)( 8,15)( 9,14)
(19,20)(22,26)(23,25)(24,27)(28,37)(29,39)(30,38)(31,43)(32,45)(33,44)(34,40)
(35,42)(36,41)(46,47)(49,53)(50,52)(51,54);
s2 := Sym(56)!( 1,31)( 2,32)( 3,33)( 4,28)( 5,29)( 6,30)( 7,34)( 8,35)( 9,36)
(10,40)(11,41)(12,42)(13,37)(14,38)(15,39)(16,43)(17,44)(18,45)(19,49)(20,50)
(21,51)(22,46)(23,47)(24,48)(25,52)(26,53)(27,54);
s3 := Sym(56)!(55,56);
poly := sub<Sym(56)|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, 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 >; 
 

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