Polytope of Type {2,10,12,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,12,2,2}*1920
if this polytope has a name.
Group : SmallGroup(1920,236182)
Rank : 6
Schlafli Type : {2,10,12,2,2}
Number of vertices, edges, etc : 2, 10, 60, 12, 2, 2
Order of s₀s₁s₂s₃s₄s₅ : 60
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 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) :
   2-fold quotients : {2,10,6,2,2}*960
   3-fold quotients : {2,10,4,2,2}*640
   5-fold quotients : {2,2,12,2,2}*384
   6-fold quotients : {2,10,2,2,2}*320
   10-fold quotients : {2,2,6,2,2}*192
   12-fold quotients : {2,5,2,2,2}*160
   15-fold quotients : {2,2,4,2,2}*128
   20-fold quotients : {2,2,3,2,2}*96
   30-fold quotients : {2,2,2,2,2}*64
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)
(29,32)(30,31)(34,37)(35,36)(39,42)(40,41)(44,47)(45,46)(49,52)(50,51)(54,57)
(55,56)(59,62)(60,61);;
s2 := ( 3, 4)( 5, 7)( 8,14)( 9,13)(10,17)(11,16)(12,15)(18,19)(20,22)(23,29)
(24,28)(25,32)(26,31)(27,30)(33,49)(34,48)(35,52)(36,51)(37,50)(38,59)(39,58)
(40,62)(41,61)(42,60)(43,54)(44,53)(45,57)(46,56)(47,55);;
s3 := ( 3,38)( 4,39)( 5,40)( 6,41)( 7,42)( 8,33)( 9,34)(10,35)(11,36)(12,37)
(13,43)(14,44)(15,45)(16,46)(17,47)(18,53)(19,54)(20,55)(21,56)(22,57)(23,48)
(24,49)(25,50)(26,51)(27,52)(28,58)(29,59)(30,60)(31,61)(32,62);;
s4 := (63,64);;
s5 := (65,66);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*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*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(66)!(1,2);
s1 := Sym(66)!( 4, 7)( 5, 6)( 9,12)(10,11)(14,17)(15,16)(19,22)(20,21)(24,27)
(25,26)(29,32)(30,31)(34,37)(35,36)(39,42)(40,41)(44,47)(45,46)(49,52)(50,51)
(54,57)(55,56)(59,62)(60,61);
s2 := Sym(66)!( 3, 4)( 5, 7)( 8,14)( 9,13)(10,17)(11,16)(12,15)(18,19)(20,22)
(23,29)(24,28)(25,32)(26,31)(27,30)(33,49)(34,48)(35,52)(36,51)(37,50)(38,59)
(39,58)(40,62)(41,61)(42,60)(43,54)(44,53)(45,57)(46,56)(47,55);
s3 := Sym(66)!( 3,38)( 4,39)( 5,40)( 6,41)( 7,42)( 8,33)( 9,34)(10,35)(11,36)
(12,37)(13,43)(14,44)(15,45)(16,46)(17,47)(18,53)(19,54)(20,55)(21,56)(22,57)
(23,48)(24,49)(25,50)(26,51)(27,52)(28,58)(29,59)(30,60)(31,61)(32,62);
s4 := Sym(66)!(63,64);
s5 := Sym(66)!(65,66);
poly := sub<Sym(66)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5, s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*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*s2*s3*s2*s3 >;

to this polytope