Polytope of Type {15,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,6,4}*1920
if this polytope has a name.
Group : SmallGroup(1920,238598)
Rank : 4
Schlafli Type : {15,6,4}
Number of vertices, edges, etc : 20, 120, 32, 8
Order of s₀s₁s₂s₃ : 20
Order of s₀s₁s₂s₃s₂s₁ : 4
Special Properties :
   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 : {15,6,2}*480
   5-fold quotients : {3,6,4}*384b
   10-fold quotients : {3,3,4}*192
   20-fold quotients : {3,6,2}*96
   40-fold quotients : {3,3,2}*48
   48-fold quotients : {5,2,2}*40
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 3, 4)( 7, 8)( 9,13)(10,14)(11,16)(12,15)(17,65)(18,66)(19,68)(20,67)
(21,69)(22,70)(23,72)(24,71)(25,77)(26,78)(27,80)(28,79)(29,73)(30,74)(31,76)
(32,75)(33,49)(34,50)(35,52)(36,51)(37,53)(38,54)(39,56)(40,55)(41,61)(42,62)
(43,64)(44,63)(45,57)(46,58)(47,60)(48,59);;
s1 := ( 1,17)( 2,20)( 3,19)( 4,18)( 5,29)( 6,32)( 7,31)( 8,30)( 9,25)(10,28)
(11,27)(12,26)(13,21)(14,24)(15,23)(16,22)(33,65)(34,68)(35,67)(36,66)(37,77)
(38,80)(39,79)(40,78)(41,73)(42,76)(43,75)(44,74)(45,69)(46,72)(47,71)(48,70)
(50,52)(53,61)(54,64)(55,63)(56,62)(58,60);;
s2 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)(11,12)(15,16)(17,21)(18,22)(19,24)(20,23)
(27,28)(31,32)(33,37)(34,38)(35,40)(36,39)(43,44)(47,48)(49,53)(50,54)(51,56)
(52,55)(59,60)(63,64)(65,69)(66,70)(67,72)(68,71)(75,76)(79,80);;
s3 := ( 5, 6)( 7, 8)( 9,11)(10,12)(13,16)(14,15)(21,22)(23,24)(25,27)(26,28)
(29,32)(30,31)(37,38)(39,40)(41,43)(42,44)(45,48)(46,47)(53,54)(55,56)(57,59)
(58,60)(61,64)(62,63)(69,70)(71,72)(73,75)(74,76)(77,80)(78,79);;
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*s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2*s0*s1, 
s1*s0*s3*s2*s1*s2*s3*s2*s3*s1*s0*s2*s1*s2*s3*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(80)!( 3, 4)( 7, 8)( 9,13)(10,14)(11,16)(12,15)(17,65)(18,66)(19,68)
(20,67)(21,69)(22,70)(23,72)(24,71)(25,77)(26,78)(27,80)(28,79)(29,73)(30,74)
(31,76)(32,75)(33,49)(34,50)(35,52)(36,51)(37,53)(38,54)(39,56)(40,55)(41,61)
(42,62)(43,64)(44,63)(45,57)(46,58)(47,60)(48,59);
s1 := Sym(80)!( 1,17)( 2,20)( 3,19)( 4,18)( 5,29)( 6,32)( 7,31)( 8,30)( 9,25)
(10,28)(11,27)(12,26)(13,21)(14,24)(15,23)(16,22)(33,65)(34,68)(35,67)(36,66)
(37,77)(38,80)(39,79)(40,78)(41,73)(42,76)(43,75)(44,74)(45,69)(46,72)(47,71)
(48,70)(50,52)(53,61)(54,64)(55,63)(56,62)(58,60);
s2 := Sym(80)!( 1, 5)( 2, 6)( 3, 8)( 4, 7)(11,12)(15,16)(17,21)(18,22)(19,24)
(20,23)(27,28)(31,32)(33,37)(34,38)(35,40)(36,39)(43,44)(47,48)(49,53)(50,54)
(51,56)(52,55)(59,60)(63,64)(65,69)(66,70)(67,72)(68,71)(75,76)(79,80);
s3 := Sym(80)!( 5, 6)( 7, 8)( 9,11)(10,12)(13,16)(14,15)(21,22)(23,24)(25,27)
(26,28)(29,32)(30,31)(37,38)(39,40)(41,43)(42,44)(45,48)(46,47)(53,54)(55,56)
(57,59)(58,60)(61,64)(62,63)(69,70)(71,72)(73,75)(74,76)(77,80)(78,79);
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, 
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2*s0*s1, 
s1*s0*s3*s2*s1*s2*s3*s2*s3*s1*s0*s2*s1*s2*s3*s2 >;

References : None.
to this polytope