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