Polytope of Type {20,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,6}*1920d
if this polytope has a name.
Group : SmallGroup(1920,240872)
Rank : 3
Schlafli Type : {20,6}
Number of vertices, edges, etc : 160, 480, 48
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 20
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {20,6}*960c, {20,6}*960d, {10,6}*960b
   4-fold quotients : {20,6}*480a, {20,6}*480b, {20,3}*480, {10,6}*480c
   8-fold quotients : {5,6}*240b, {10,3}*240, {10,6}*240c, {10,6}*240d, {10,6}*240e, {10,6}*240f
   16-fold quotients : {5,3}*120, {5,6}*120b, {5,6}*120c, {10,3}*120a, {10,3}*120b
   32-fold quotients : {5,3}*60
   120-fold quotients : {4,2}*16
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 3, 4)( 7,10)( 8, 9)(11,12)(13,15)(14,16)(17,22)(18,21)(23,24)(25,28)
(26,27)(29,30)(33,34)(35,37)(36,38)(41,44)(42,43)(45,49)(46,50)(47,48)(53,55)
(54,56);;
s1 := ( 1,29)( 2,30)( 3,31)( 4,32)( 5,35)( 6,36)( 7,34)( 8,33)( 9,49)(10,50)
(11,52)(12,51)(13,55)(14,56)(15,46)(16,45)(17,43)(18,44)(19,53)(20,54)(21,38)
(22,37)(23,39)(24,40)(25,48)(26,47)(27,42)(28,41);;
s2 := ( 1,31)( 2,32)( 3,29)( 4,30)( 5,51)( 6,52)( 7,53)( 8,54)( 9,56)(10,55)
(11,47)(12,48)(13,44)(14,43)(15,41)(16,42)(17,50)(18,49)(19,40)(20,39)(21,45)
(22,46)(23,34)(24,33)(25,36)(26,35)(27,37)(28,38);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1, 
s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(56)!( 3, 4)( 7,10)( 8, 9)(11,12)(13,15)(14,16)(17,22)(18,21)(23,24)
(25,28)(26,27)(29,30)(33,34)(35,37)(36,38)(41,44)(42,43)(45,49)(46,50)(47,48)
(53,55)(54,56);
s1 := Sym(56)!( 1,29)( 2,30)( 3,31)( 4,32)( 5,35)( 6,36)( 7,34)( 8,33)( 9,49)
(10,50)(11,52)(12,51)(13,55)(14,56)(15,46)(16,45)(17,43)(18,44)(19,53)(20,54)
(21,38)(22,37)(23,39)(24,40)(25,48)(26,47)(27,42)(28,41);
s2 := Sym(56)!( 1,31)( 2,32)( 3,29)( 4,30)( 5,51)( 6,52)( 7,53)( 8,54)( 9,56)
(10,55)(11,47)(12,48)(13,44)(14,43)(15,41)(16,42)(17,50)(18,49)(19,40)(20,39)
(21,45)(22,46)(23,34)(24,33)(25,36)(26,35)(27,37)(28,38);
poly := sub<Sym(56)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1, 
s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1 >;

References : None.
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