Polytope of Type {12,2,40}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,2,40}*1920
if this polytope has a name.
Group : SmallGroup(1920,182161)
Rank : 4
Schlafli Type : {12,2,40}
Number of vertices, edges, etc : 12, 12, 40, 40
Order of s₀s₁s₂s₃ : 120
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 : {12,2,20}*960, {6,2,40}*960
   3-fold quotients : {4,2,40}*640
   4-fold quotients : {3,2,40}*480, {12,2,10}*480, {6,2,20}*480
   5-fold quotients : {12,2,8}*384
   6-fold quotients : {4,2,20}*320, {2,2,40}*320
   8-fold quotients : {12,2,5}*240, {3,2,20}*240, {6,2,10}*240
   10-fold quotients : {12,2,4}*192, {6,2,8}*192
   12-fold quotients : {2,2,20}*160, {4,2,10}*160
   15-fold quotients : {4,2,8}*128
   16-fold quotients : {3,2,10}*120, {6,2,5}*120
   20-fold quotients : {3,2,8}*96, {12,2,2}*96, {6,2,4}*96
   24-fold quotients : {4,2,5}*80, {2,2,10}*80
   30-fold quotients : {4,2,4}*64, {2,2,8}*64
   32-fold quotients : {3,2,5}*60
   40-fold quotients : {3,2,4}*48, {6,2,2}*48
   48-fold quotients : {2,2,5}*40
   60-fold quotients : {2,2,4}*32, {4,2,2}*32
   80-fold quotients : {3,2,2}*24
   120-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 := (14,15)(16,17)(18,21)(19,23)(20,22)(24,25)(26,31)(27,33)(28,32)(29,35)
(30,34)(37,42)(38,41)(39,44)(40,43)(45,46)(47,50)(48,49)(51,52);;
s3 := (13,19)(14,16)(15,27)(17,29)(18,22)(20,24)(21,37)(23,39)(25,30)(26,32)
(28,34)(31,45)(33,47)(35,40)(36,41)(38,43)(42,51)(44,48)(46,49)(50,52);;
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*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(52)!( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12);
s1 := Sym(52)!( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);
s2 := Sym(52)!(14,15)(16,17)(18,21)(19,23)(20,22)(24,25)(26,31)(27,33)(28,32)
(29,35)(30,34)(37,42)(38,41)(39,44)(40,43)(45,46)(47,50)(48,49)(51,52);
s3 := Sym(52)!(13,19)(14,16)(15,27)(17,29)(18,22)(20,24)(21,37)(23,39)(25,30)
(26,32)(28,34)(31,45)(33,47)(35,40)(36,41)(38,43)(42,51)(44,48)(46,49)(50,52);
poly := sub<Sym(52)|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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope