Polytope of Type {2,14,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,14,6}*336
if this polytope has a name.
Group : SmallGroup(336,219)
Rank : 4
Schlafli Type : {2,14,6}
Number of vertices, edges, etc : 2, 14, 42, 6
Order of s₀s₁s₂s₃ : 42
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,14,6,2} of size 672
   {2,14,6,3} of size 1008
   {2,14,6,4} of size 1344
   {2,14,6,3} of size 1344
   {2,14,6,4} of size 1344
Vertex Figure Of :
   {2,2,14,6} of size 672
   {3,2,14,6} of size 1008
   {4,2,14,6} of size 1344
   {5,2,14,6} of size 1680
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,14,2}*112
   6-fold quotients : {2,7,2}*56
   7-fold quotients : {2,2,6}*48
   14-fold quotients : {2,2,3}*24
   21-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,14,12}*672, {2,28,6}*672a, {4,14,6}*672
   3-fold covers : {2,14,18}*1008, {6,14,6}*1008, {2,42,6}*1008a, {2,42,6}*1008b
   4-fold covers : {4,14,12}*1344, {4,28,6}*1344, {2,14,24}*1344, {2,56,6}*1344, {8,14,6}*1344, {2,28,12}*1344, {2,28,6}*1344
   5-fold covers : {10,14,6}*1680, {2,14,30}*1680, {2,70,6}*1680
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 9)( 5, 8)( 6, 7)(11,16)(12,15)(13,14)(18,23)(19,22)(20,21)(25,30)
(26,29)(27,28)(32,37)(33,36)(34,35)(39,44)(40,43)(41,42)(46,51)(47,50)(48,49)
(53,58)(54,57)(55,56)(60,65)(61,64)(62,63)(67,72)(68,71)(69,70)(74,79)(75,78)
(76,77)(81,86)(82,85)(83,84);;
s2 := ( 3,46)( 4,45)( 5,51)( 6,50)( 7,49)( 8,48)( 9,47)(10,60)(11,59)(12,65)
(13,64)(14,63)(15,62)(16,61)(17,53)(18,52)(19,58)(20,57)(21,56)(22,55)(23,54)
(24,67)(25,66)(26,72)(27,71)(28,70)(29,69)(30,68)(31,81)(32,80)(33,86)(34,85)
(35,84)(36,83)(37,82)(38,74)(39,73)(40,79)(41,78)(42,77)(43,76)(44,75);;
s3 := ( 3,73)( 4,74)( 5,75)( 6,76)( 7,77)( 8,78)( 9,79)(10,66)(11,67)(12,68)
(13,69)(14,70)(15,71)(16,72)(17,80)(18,81)(19,82)(20,83)(21,84)(22,85)(23,86)
(24,52)(25,53)(26,54)(27,55)(28,56)(29,57)(30,58)(31,45)(32,46)(33,47)(34,48)
(35,49)(36,50)(37,51)(38,59)(39,60)(40,61)(41,62)(42,63)(43,64)(44,65);;
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, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*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(86)!(1,2);
s1 := Sym(86)!( 4, 9)( 5, 8)( 6, 7)(11,16)(12,15)(13,14)(18,23)(19,22)(20,21)
(25,30)(26,29)(27,28)(32,37)(33,36)(34,35)(39,44)(40,43)(41,42)(46,51)(47,50)
(48,49)(53,58)(54,57)(55,56)(60,65)(61,64)(62,63)(67,72)(68,71)(69,70)(74,79)
(75,78)(76,77)(81,86)(82,85)(83,84);
s2 := Sym(86)!( 3,46)( 4,45)( 5,51)( 6,50)( 7,49)( 8,48)( 9,47)(10,60)(11,59)
(12,65)(13,64)(14,63)(15,62)(16,61)(17,53)(18,52)(19,58)(20,57)(21,56)(22,55)
(23,54)(24,67)(25,66)(26,72)(27,71)(28,70)(29,69)(30,68)(31,81)(32,80)(33,86)
(34,85)(35,84)(36,83)(37,82)(38,74)(39,73)(40,79)(41,78)(42,77)(43,76)(44,75);
s3 := Sym(86)!( 3,73)( 4,74)( 5,75)( 6,76)( 7,77)( 8,78)( 9,79)(10,66)(11,67)
(12,68)(13,69)(14,70)(15,71)(16,72)(17,80)(18,81)(19,82)(20,83)(21,84)(22,85)
(23,86)(24,52)(25,53)(26,54)(27,55)(28,56)(29,57)(30,58)(31,45)(32,46)(33,47)
(34,48)(35,49)(36,50)(37,51)(38,59)(39,60)(40,61)(41,62)(42,63)(43,64)(44,65);
poly := sub<Sym(86)|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, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope