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Polytope of Type {2,30,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,30,10}*1200a
if this polytope has a name.
Group : SmallGroup(1200,1006)
Rank : 4
Schlafli Type : {2,30,10}
Number of vertices, edges, etc : 2, 30, 150, 10
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,10,10}*400b
   5-fold quotients : {2,6,10}*240
   6-fold quotients : {2,10,5}*200
   15-fold quotients : {2,2,10}*80
   25-fold quotients : {2,6,2}*48
   30-fold quotients : {2,2,5}*40
   50-fold quotients : {2,3,2}*24
   75-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 7)( 5, 6)( 9,12)(10,11)(14,17)(15,16)(19,22)(20,21)(24,27)(25,26)
(28,53)(29,57)(30,56)(31,55)(32,54)(33,58)(34,62)(35,61)(36,60)(37,59)(38,63)
(39,67)(40,66)(41,65)(42,64)(43,68)(44,72)(45,71)(46,70)(47,69)(48,73)(49,77)
(50,76)(51,75)(52,74);;
s2 := ( 3,29)( 4,28)( 5,32)( 6,31)( 7,30)( 8,49)( 9,48)(10,52)(11,51)(12,50)
(13,44)(14,43)(15,47)(16,46)(17,45)(18,39)(19,38)(20,42)(21,41)(22,40)(23,34)
(24,33)(25,37)(26,36)(27,35)(53,54)(55,57)(58,74)(59,73)(60,77)(61,76)(62,75)
(63,69)(64,68)(65,72)(66,71)(67,70);;
s3 := ( 3, 8)( 4,12)( 5,11)( 6,10)( 7, 9)(13,23)(14,27)(15,26)(16,25)(17,24)
(19,22)(20,21)(28,33)(29,37)(30,36)(31,35)(32,34)(38,48)(39,52)(40,51)(41,50)
(42,49)(44,47)(45,46)(53,58)(54,62)(55,61)(56,60)(57,59)(63,73)(64,77)(65,76)
(66,75)(67,74)(69,72)(70,71);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s3*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(77)!(1,2);
s1 := Sym(77)!( 4, 7)( 5, 6)( 9,12)(10,11)(14,17)(15,16)(19,22)(20,21)(24,27)
(25,26)(28,53)(29,57)(30,56)(31,55)(32,54)(33,58)(34,62)(35,61)(36,60)(37,59)
(38,63)(39,67)(40,66)(41,65)(42,64)(43,68)(44,72)(45,71)(46,70)(47,69)(48,73)
(49,77)(50,76)(51,75)(52,74);
s2 := Sym(77)!( 3,29)( 4,28)( 5,32)( 6,31)( 7,30)( 8,49)( 9,48)(10,52)(11,51)
(12,50)(13,44)(14,43)(15,47)(16,46)(17,45)(18,39)(19,38)(20,42)(21,41)(22,40)
(23,34)(24,33)(25,37)(26,36)(27,35)(53,54)(55,57)(58,74)(59,73)(60,77)(61,76)
(62,75)(63,69)(64,68)(65,72)(66,71)(67,70);
s3 := Sym(77)!( 3, 8)( 4,12)( 5,11)( 6,10)( 7, 9)(13,23)(14,27)(15,26)(16,25)
(17,24)(19,22)(20,21)(28,33)(29,37)(30,36)(31,35)(32,34)(38,48)(39,52)(40,51)
(41,50)(42,49)(44,47)(45,46)(53,58)(54,62)(55,61)(56,60)(57,59)(63,73)(64,77)
(65,76)(66,75)(67,74)(69,72)(70,71);
poly := sub<Sym(77)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s3*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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