Polytope of Type {2,4,14,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,14,6}*1344
if this polytope has a name.
Group : SmallGroup(1344,11527)
Rank : 5
Schlafli Type : {2,4,14,6}
Number of vertices, edges, etc : 2, 4, 28, 42, 6
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 : {2,2,14,6}*672
3-fold quotients : {2,4,14,2}*448
6-fold quotients : {2,2,14,2}*224
7-fold quotients : {2,4,2,6}*192
12-fold quotients : {2,2,7,2}*112
14-fold quotients : {2,4,2,3}*96, {2,2,2,6}*96
21-fold quotients : {2,4,2,2}*64
28-fold quotients : {2,2,2,3}*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)( 4,51)( 5,50)( 6,49)( 7,48)( 8,47)( 9,46)(10,52)(11,58)(12,57)
(13,56)(14,55)(15,54)(16,53)(17,59)(18,65)(19,64)(20,63)(21,62)(22,61)(23,60)
(24,66)(25,72)(26,71)(27,70)(28,69)(29,68)(30,67)(31,73)(32,79)(33,78)(34,77)
(35,76)(36,75)(37,74)(38,80)(39,86)(40,85)(41,84)(42,83)(43,82)(44,81);;
s3 := ( 3, 4)( 5, 9)( 6, 8)(10,18)(11,17)(12,23)(13,22)(14,21)(15,20)(16,19)
(24,25)(26,30)(27,29)(31,39)(32,38)(33,44)(34,43)(35,42)(36,41)(37,40)(45,46)
(47,51)(48,50)(52,60)(53,59)(54,65)(55,64)(56,63)(57,62)(58,61)(66,67)(68,72)
(69,71)(73,81)(74,80)(75,86)(76,85)(77,84)(78,83)(79,82);;
s4 := ( 3,10)( 4,11)( 5,12)( 6,13)( 7,14)( 8,15)( 9,16)(24,31)(25,32)(26,33)
(27,34)(28,35)(29,36)(30,37)(45,52)(46,53)(47,54)(48,55)(49,56)(50,57)(51,58)
(66,73)(67,74)(68,75)(69,76)(70,77)(71,78)(72,79);;
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, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
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(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)( 4,51)( 5,50)( 6,49)( 7,48)( 8,47)( 9,46)(10,52)(11,58)
(12,57)(13,56)(14,55)(15,54)(16,53)(17,59)(18,65)(19,64)(20,63)(21,62)(22,61)
(23,60)(24,66)(25,72)(26,71)(27,70)(28,69)(29,68)(30,67)(31,73)(32,79)(33,78)
(34,77)(35,76)(36,75)(37,74)(38,80)(39,86)(40,85)(41,84)(42,83)(43,82)(44,81);
s3 := Sym(86)!( 3, 4)( 5, 9)( 6, 8)(10,18)(11,17)(12,23)(13,22)(14,21)(15,20)
(16,19)(24,25)(26,30)(27,29)(31,39)(32,38)(33,44)(34,43)(35,42)(36,41)(37,40)
(45,46)(47,51)(48,50)(52,60)(53,59)(54,65)(55,64)(56,63)(57,62)(58,61)(66,67)
(68,72)(69,71)(73,81)(74,80)(75,86)(76,85)(77,84)(78,83)(79,82);
s4 := Sym(86)!( 3,10)( 4,11)( 5,12)( 6,13)( 7,14)( 8,15)( 9,16)(24,31)(25,32)
(26,33)(27,34)(28,35)(29,36)(30,37)(45,52)(46,53)(47,54)(48,55)(49,56)(50,57)
(51,58)(66,73)(67,74)(68,75)(69,76)(70,77)(71,78)(72,79);
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,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
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