Polytope of Type {20,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,12}*1920m
if this polytope has a name.
Group : SmallGroup(1920,240875)
Rank : 3
Schlafli Type : {20,12}
Number of vertices, edges, etc : 80, 480, 48
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 20
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {10,12}*960d, {20,6}*960d
   4-fold quotients : {5,12}*480, {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
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
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