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

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

Permutation Representation (Magma) :

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

to this polytope