Polytope of Type {12,2,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,2,30}*1440
if this polytope has a name.
Group : SmallGroup(1440,5675)
Rank : 4
Schlafli Type : {12,2,30}
Number of vertices, edges, etc : 12, 12, 30, 30
Order of s₀s₁s₂s₃ : 60
Order of s₀s₁s₂s₃s₂s₁ : 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 : {12,2,15}*720, {6,2,30}*720
   3-fold quotients : {12,2,10}*480, {4,2,30}*480
   4-fold quotients : {3,2,30}*360, {6,2,15}*360
   5-fold quotients : {12,2,6}*288
   6-fold quotients : {12,2,5}*240, {4,2,15}*240, {6,2,10}*240, {2,2,30}*240
   8-fold quotients : {3,2,15}*180
   9-fold quotients : {4,2,10}*160
   10-fold quotients : {12,2,3}*144, {6,2,6}*144
   12-fold quotients : {3,2,10}*120, {6,2,5}*120, {2,2,15}*120
   15-fold quotients : {12,2,2}*96, {4,2,6}*96
   18-fold quotients : {4,2,5}*80, {2,2,10}*80
   20-fold quotients : {3,2,6}*72, {6,2,3}*72
   24-fold quotients : {3,2,5}*60
   30-fold quotients : {4,2,3}*48, {2,2,6}*48, {6,2,2}*48
   36-fold quotients : {2,2,5}*40
   40-fold quotients : {3,2,3}*36
   45-fold quotients : {4,2,2}*32
   60-fold quotients : {2,2,3}*24, {3,2,2}*24
   90-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12);;
s1 := ( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);;
s2 := (15,16)(17,18)(19,20)(21,22)(23,26)(24,25)(27,28)(29,32)(30,31)(33,34)
(35,38)(36,37)(39,42)(40,41);;
s3 := (13,29)(14,23)(15,21)(16,31)(17,19)(18,39)(20,25)(22,35)(24,33)(26,41)
(27,30)(28,40)(32,37)(34,36)(38,42);;
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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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(42)!( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12);
s1 := Sym(42)!( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);
s2 := Sym(42)!(15,16)(17,18)(19,20)(21,22)(23,26)(24,25)(27,28)(29,32)(30,31)
(33,34)(35,38)(36,37)(39,42)(40,41);
s3 := Sym(42)!(13,29)(14,23)(15,21)(16,31)(17,19)(18,39)(20,25)(22,35)(24,33)
(26,41)(27,30)(28,40)(32,37)(34,36)(38,42);
poly := sub<Sym(42)|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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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