Polytope of Type {42,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {42,2}*168
if this polytope has a name.
Group : SmallGroup(168,56)
Rank : 3
Schlafli Type : {42,2}
Number of vertices, edges, etc : 42, 42, 2
Order of s₀s₁s₂ : 42
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {42,2,2} of size 336
   {42,2,3} of size 504
   {42,2,4} of size 672
   {42,2,5} of size 840
   {42,2,6} of size 1008
   {42,2,7} of size 1176
   {42,2,8} of size 1344
   {42,2,9} of size 1512
   {42,2,10} of size 1680
   {42,2,11} of size 1848
Vertex Figure Of :
   {2,42,2} of size 336
   {4,42,2} of size 672
   {4,42,2} of size 672
   {4,42,2} of size 672
   {6,42,2} of size 1008
   {6,42,2} of size 1008
   {6,42,2} of size 1008
   {8,42,2} of size 1344
   {6,42,2} of size 1344
   {4,42,2} of size 1344
   {6,42,2} of size 1512
   {10,42,2} of size 1680
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {21,2}*84
   3-fold quotients : {14,2}*56
   6-fold quotients : {7,2}*28
   7-fold quotients : {6,2}*24
   14-fold quotients : {3,2}*12
   21-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {84,2}*336, {42,4}*336a
   3-fold covers : {126,2}*504, {42,6}*504b, {42,6}*504c
   4-fold covers : {84,4}*672a, {168,2}*672, {42,8}*672, {42,4}*672
   5-fold covers : {42,10}*840, {210,2}*840
   6-fold covers : {252,2}*1008, {126,4}*1008a, {42,12}*1008b, {84,6}*1008b, {84,6}*1008c, {42,12}*1008c
   7-fold covers : {294,2}*1176, {42,14}*1176b, {42,14}*1176c
   8-fold covers : {168,4}*1344a, {84,4}*1344a, {168,4}*1344b, {84,8}*1344a, {84,8}*1344b, {336,2}*1344, {42,16}*1344, {84,4}*1344b, {42,4}*1344b, {84,4}*1344c, {42,8}*1344b, {42,8}*1344c
   9-fold covers : {378,2}*1512, {126,6}*1512a, {126,6}*1512b, {42,18}*1512b, {42,6}*1512b, {42,6}*1512c, {42,6}*1512d
   10-fold covers : {42,20}*1680a, {84,10}*1680, {420,2}*1680, {210,4}*1680a
   11-fold covers : {42,22}*1848, {462,2}*1848
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

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

to this polytope