Polytope of Type {2,30,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,30,12}*1440d
if this polytope has a name.
Group : SmallGroup(1440,5900)
Rank : 4
Schlafli Type : {2,30,12}
Number of vertices, edges, etc : 2, 30, 180, 12
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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) :
   3-fold quotients : {2,30,4}*480c
   5-fold quotients : {2,6,12}*288d
   6-fold quotients : {2,15,4}*240
   15-fold quotients : {2,6,4}*96b
   30-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Finitely Presented Group Representation (Magma) :

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

to this polytope