Polytope of Type {3,2,42}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,42}*504
if this polytope has a name.
Group : SmallGroup(504,192)
Rank : 4
Schlafli Type : {3,2,42}
Number of vertices, edges, etc : 3, 3, 42, 42
Order of s₀s₁s₂s₃ : 42
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,42,2} of size 1008
Vertex Figure Of :
   {2,3,2,42} of size 1008
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,21}*252
   3-fold quotients : {3,2,14}*168
   6-fold quotients : {3,2,7}*84
   7-fold quotients : {3,2,6}*72
   14-fold quotients : {3,2,3}*36
   21-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,84}*1008, {6,2,42}*1008
   3-fold covers : {3,2,126}*1512, {9,2,42}*1512, {3,6,42}*1512a, {3,6,42}*1512b
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := ( 6, 7)( 8, 9)(10,11)(12,13)(14,17)(15,16)(18,19)(20,23)(21,22)(24,25)
(26,29)(27,28)(30,31)(32,35)(33,34)(36,37)(38,41)(39,40)(42,45)(43,44);;
s3 := ( 4,20)( 5,14)( 6,12)( 7,22)( 8,10)( 9,32)(11,16)(13,26)(15,24)(17,34)
(18,21)(19,42)(23,28)(25,38)(27,36)(29,44)(30,33)(31,43)(35,40)(37,39)
(41,45);;
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, 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*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(45)!(2,3);
s1 := Sym(45)!(1,2);
s2 := Sym(45)!( 6, 7)( 8, 9)(10,11)(12,13)(14,17)(15,16)(18,19)(20,23)(21,22)
(24,25)(26,29)(27,28)(30,31)(32,35)(33,34)(36,37)(38,41)(39,40)(42,45)(43,44);
s3 := Sym(45)!( 4,20)( 5,14)( 6,12)( 7,22)( 8,10)( 9,32)(11,16)(13,26)(15,24)
(17,34)(18,21)(19,42)(23,28)(25,38)(27,36)(29,44)(30,33)(31,43)(35,40)(37,39)
(41,45);
poly := sub<Sym(45)|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, 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*s2*s3*s2*s3 >;

to this polytope