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

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

Permutation Representation (Magma) :

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

to this polytope