Overview
- Group
- SmallGroup(672,1150)
- Rank
- 4
- Schläfli Type
- {4,14,6}
- Vertices, edges, …
- 4, 28, 42, 6
- Order of s0s1s2s3
- 84
- Order of s0s1s2s3s2s1
- 2
- Also known as
- {{4,14|2},{14,6|2}}. if this polytope has another name.
Special Properties
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
6-fold
7-fold
12-fold
14-fold
21-fold
28-fold
42-fold
Covers minimal covers in bold
2-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
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)( 2,49)( 3,48)( 4,47)( 5,46)( 6,45)( 7,44)( 8,50)( 9,56)(10,55)(11,54)(12,53)(13,52)(14,51)(15,57)(16,63)(17,62)(18,61)(19,60)(20,59)(21,58)(22,64)(23,70)(24,69)(25,68)(26,67)(27,66)(28,65)(29,71)(30,77)(31,76)(32,75)(33,74)(34,73)(35,72)(36,78)(37,84)(38,83)(39,82)(40,81)(41,80)(42,79);; s2 := ( 1, 2)( 3, 7)( 4, 6)( 8,16)( 9,15)(10,21)(11,20)(12,19)(13,18)(14,17)(22,23)(24,28)(25,27)(29,37)(30,36)(31,42)(32,41)(33,40)(34,39)(35,38)(43,44)(45,49)(46,48)(50,58)(51,57)(52,63)(53,62)(54,61)(55,60)(56,59)(64,65)(66,70)(67,69)(71,79)(72,78)(73,84)(74,83)(75,82)(76,81)(77,80);; s3 := ( 1, 8)( 2, 9)( 3,10)( 4,11)( 5,12)( 6,13)( 7,14)(22,29)(23,30)(24,31)(25,32)(26,33)(27,34)(28,35)(43,50)(44,51)(45,52)(46,53)(47,54)(48,55)(49,56)(64,71)(65,72)(66,73)(67,74)(68,75)(69,76)(70,77);; 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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, 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(84)!(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(84)!( 1,43)( 2,49)( 3,48)( 4,47)( 5,46)( 6,45)( 7,44)( 8,50)( 9,56)(10,55)(11,54)(12,53)(13,52)(14,51)(15,57)(16,63)(17,62)(18,61)(19,60)(20,59)(21,58)(22,64)(23,70)(24,69)(25,68)(26,67)(27,66)(28,65)(29,71)(30,77)(31,76)(32,75)(33,74)(34,73)(35,72)(36,78)(37,84)(38,83)(39,82)(40,81)(41,80)(42,79); s2 := Sym(84)!( 1, 2)( 3, 7)( 4, 6)( 8,16)( 9,15)(10,21)(11,20)(12,19)(13,18)(14,17)(22,23)(24,28)(25,27)(29,37)(30,36)(31,42)(32,41)(33,40)(34,39)(35,38)(43,44)(45,49)(46,48)(50,58)(51,57)(52,63)(53,62)(54,61)(55,60)(56,59)(64,65)(66,70)(67,69)(71,79)(72,78)(73,84)(74,83)(75,82)(76,81)(77,80); s3 := Sym(84)!( 1, 8)( 2, 9)( 3,10)( 4,11)( 5,12)( 6,13)( 7,14)(22,29)(23,30)(24,31)(25,32)(26,33)(27,34)(28,35)(43,50)(44,51)(45,52)(46,53)(47,54)(48,55)(49,56)(64,71)(65,72)(66,73)(67,74)(68,75)(69,76)(70,77); poly := sub<Sym(84)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 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 >;
References
None.
to this polytope.