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Polytope of Type {4,6,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,10}*1920a
if this polytope has a name.
Group : SmallGroup(1920,238598)
Rank : 4
Schlafli Type : {4,6,10}
Number of vertices, edges, etc : 16, 48, 120, 10
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Universal
   Non-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) :
   4-fold quotients : {4,6,10}*480b
   5-fold quotients : {4,6,2}*384a
   20-fold quotients : {4,6,2}*96c
   40-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 9)( 2,10)( 3,11)( 4,12)( 5,13)( 6,14)( 7,15)( 8,16)(17,25)(18,26)
(19,27)(20,28)(21,29)(22,30)(23,31)(24,32)(33,41)(34,42)(35,43)(36,44)(37,45)
(38,46)(39,47)(40,48)(49,57)(50,58)(51,59)(52,60)(53,61)(54,62)(55,63)(56,64)
(65,73)(66,74)(67,75)(68,76)(69,77)(70,78)(71,79)(72,80);;
s1 := ( 3, 4)( 5, 6)( 9,16)(10,15)(11,13)(12,14)(19,20)(21,22)(25,32)(26,31)
(27,29)(28,30)(35,36)(37,38)(41,48)(42,47)(43,45)(44,46)(51,52)(53,54)(57,64)
(58,63)(59,61)(60,62)(67,68)(69,70)(73,80)(74,79)(75,77)(76,78);;
s2 := ( 2, 4)( 5,13)( 6,16)( 7,15)( 8,14)(10,12)(17,65)(18,68)(19,67)(20,66)
(21,77)(22,80)(23,79)(24,78)(25,73)(26,76)(27,75)(28,74)(29,69)(30,72)(31,71)
(32,70)(33,49)(34,52)(35,51)(36,50)(37,61)(38,64)(39,63)(40,62)(41,57)(42,60)
(43,59)(44,58)(45,53)(46,56)(47,55)(48,54);;
s3 := ( 1,17)( 2,18)( 3,19)( 4,20)( 5,21)( 6,22)( 7,23)( 8,24)( 9,25)(10,26)
(11,27)(12,28)(13,29)(14,30)(15,31)(16,32)(33,65)(34,66)(35,67)(36,68)(37,69)
(38,70)(39,71)(40,72)(41,73)(42,74)(43,75)(44,76)(45,77)(46,78)(47,79)
(48,80);;
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*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(80)!( 1, 9)( 2,10)( 3,11)( 4,12)( 5,13)( 6,14)( 7,15)( 8,16)(17,25)
(18,26)(19,27)(20,28)(21,29)(22,30)(23,31)(24,32)(33,41)(34,42)(35,43)(36,44)
(37,45)(38,46)(39,47)(40,48)(49,57)(50,58)(51,59)(52,60)(53,61)(54,62)(55,63)
(56,64)(65,73)(66,74)(67,75)(68,76)(69,77)(70,78)(71,79)(72,80);
s1 := Sym(80)!( 3, 4)( 5, 6)( 9,16)(10,15)(11,13)(12,14)(19,20)(21,22)(25,32)
(26,31)(27,29)(28,30)(35,36)(37,38)(41,48)(42,47)(43,45)(44,46)(51,52)(53,54)
(57,64)(58,63)(59,61)(60,62)(67,68)(69,70)(73,80)(74,79)(75,77)(76,78);
s2 := Sym(80)!( 2, 4)( 5,13)( 6,16)( 7,15)( 8,14)(10,12)(17,65)(18,68)(19,67)
(20,66)(21,77)(22,80)(23,79)(24,78)(25,73)(26,76)(27,75)(28,74)(29,69)(30,72)
(31,71)(32,70)(33,49)(34,52)(35,51)(36,50)(37,61)(38,64)(39,63)(40,62)(41,57)
(42,60)(43,59)(44,58)(45,53)(46,56)(47,55)(48,54);
s3 := Sym(80)!( 1,17)( 2,18)( 3,19)( 4,20)( 5,21)( 6,22)( 7,23)( 8,24)( 9,25)
(10,26)(11,27)(12,28)(13,29)(14,30)(15,31)(16,32)(33,65)(34,66)(35,67)(36,68)
(37,69)(38,70)(39,71)(40,72)(41,73)(42,74)(43,75)(44,76)(45,77)(46,78)(47,79)
(48,80);
poly := sub<Sym(80)|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, 
s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 
References : None.
to this polytope