Polytope of Type {2,4,6,14}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,6,14}*1344a
if this polytope has a name.
Group : SmallGroup(1344,11527)
Rank : 5
Schlafli Type : {2,4,6,14}
Number of vertices, edges, etc : 2, 4, 12, 42, 14
Order of s0s1s2s3s4 : 84
Order of s0s1s2s3s4s3s2s1 : 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 : {2,2,6,14}*672
3-fold quotients : {2,4,2,14}*448
6-fold quotients : {2,4,2,7}*224, {2,2,2,14}*224
7-fold quotients : {2,4,6,2}*192a
12-fold quotients : {2,2,2,7}*112
14-fold quotients : {2,2,6,2}*96
21-fold quotients : {2,4,2,2}*64
28-fold quotients : {2,2,3,2}*48
42-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (45,66)(46,67)(47,68)(48,69)(49,70)(50,71)(51,72)(52,73)(53,74)(54,75)
(55,76)(56,77)(57,78)(58,79)(59,80)(60,81)(61,82)(62,83)(63,84)(64,85)
(65,86);;
s2 := ( 3,45)( 4,46)( 5,47)( 6,48)( 7,49)( 8,50)( 9,51)(10,59)(11,60)(12,61)
(13,62)(14,63)(15,64)(16,65)(17,52)(18,53)(19,54)(20,55)(21,56)(22,57)(23,58)
(24,66)(25,67)(26,68)(27,69)(28,70)(29,71)(30,72)(31,80)(32,81)(33,82)(34,83)
(35,84)(36,85)(37,86)(38,73)(39,74)(40,75)(41,76)(42,77)(43,78)(44,79);;
s3 := ( 3,10)( 4,16)( 5,15)( 6,14)( 7,13)( 8,12)( 9,11)(18,23)(19,22)(20,21)
(24,31)(25,37)(26,36)(27,35)(28,34)(29,33)(30,32)(39,44)(40,43)(41,42)(45,52)
(46,58)(47,57)(48,56)(49,55)(50,54)(51,53)(60,65)(61,64)(62,63)(66,73)(67,79)
(68,78)(69,77)(70,76)(71,75)(72,74)(81,86)(82,85)(83,84);;
s4 := ( 3, 4)( 5, 9)( 6, 8)(10,11)(12,16)(13,15)(17,18)(19,23)(20,22)(24,25)
(26,30)(27,29)(31,32)(33,37)(34,36)(38,39)(40,44)(41,43)(45,46)(47,51)(48,50)
(52,53)(54,58)(55,57)(59,60)(61,65)(62,64)(66,67)(68,72)(69,71)(73,74)(75,79)
(76,78)(80,81)(82,86)(83,85);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(86)!(1,2);
s1 := Sym(86)!(45,66)(46,67)(47,68)(48,69)(49,70)(50,71)(51,72)(52,73)(53,74)
(54,75)(55,76)(56,77)(57,78)(58,79)(59,80)(60,81)(61,82)(62,83)(63,84)(64,85)
(65,86);
s2 := Sym(86)!( 3,45)( 4,46)( 5,47)( 6,48)( 7,49)( 8,50)( 9,51)(10,59)(11,60)
(12,61)(13,62)(14,63)(15,64)(16,65)(17,52)(18,53)(19,54)(20,55)(21,56)(22,57)
(23,58)(24,66)(25,67)(26,68)(27,69)(28,70)(29,71)(30,72)(31,80)(32,81)(33,82)
(34,83)(35,84)(36,85)(37,86)(38,73)(39,74)(40,75)(41,76)(42,77)(43,78)(44,79);
s3 := Sym(86)!( 3,10)( 4,16)( 5,15)( 6,14)( 7,13)( 8,12)( 9,11)(18,23)(19,22)
(20,21)(24,31)(25,37)(26,36)(27,35)(28,34)(29,33)(30,32)(39,44)(40,43)(41,42)
(45,52)(46,58)(47,57)(48,56)(49,55)(50,54)(51,53)(60,65)(61,64)(62,63)(66,73)
(67,79)(68,78)(69,77)(70,76)(71,75)(72,74)(81,86)(82,85)(83,84);
s4 := Sym(86)!( 3, 4)( 5, 9)( 6, 8)(10,11)(12,16)(13,15)(17,18)(19,23)(20,22)
(24,25)(26,30)(27,29)(31,32)(33,37)(34,36)(38,39)(40,44)(41,43)(45,46)(47,51)
(48,50)(52,53)(54,58)(55,57)(59,60)(61,65)(62,64)(66,67)(68,72)(69,71)(73,74)
(75,79)(76,78)(80,81)(82,86)(83,85);
poly := sub<Sym(86)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope