Overview
- Group
- SmallGroup(1280,1036282)
- Rank
- 5
- Schläfli Type
- {2,4,20,2}
- Vertices, edges, …
- 2, 8, 80, 40, 2
- Order of s0s1s2s3s4
- 20
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
4-fold
5-fold
8-fold
10-fold
16-fold
20-fold
40-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := (23,28)(24,29)(25,30)(26,31)(27,32)(33,38)(34,39)(35,40)(36,41)(37,42)(43,53)(44,54)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(51,61)(52,62)(63,78)(64,79)(65,80)(66,81)(67,82)(68,73)(69,74)(70,75)(71,76)(72,77);; s2 := ( 3,43)( 4,47)( 5,46)( 6,45)( 7,44)( 8,48)( 9,52)(10,51)(11,50)(12,49)(13,53)(14,57)(15,56)(16,55)(17,54)(18,58)(19,62)(20,61)(21,60)(22,59)(23,63)(24,67)(25,66)(26,65)(27,64)(28,68)(29,72)(30,71)(31,70)(32,69)(33,73)(34,77)(35,76)(36,75)(37,74)(38,78)(39,82)(40,81)(41,80)(42,79);; s3 := ( 3, 4)( 5, 7)( 8, 9)(10,12)(13,19)(14,18)(15,22)(16,21)(17,20)(23,24)(25,27)(28,29)(30,32)(33,39)(34,38)(35,42)(36,41)(37,40)(43,64)(44,63)(45,67)(46,66)(47,65)(48,69)(49,68)(50,72)(51,71)(52,70)(53,79)(54,78)(55,82)(56,81)(57,80)(58,74)(59,73)(60,77)(61,76)(62,75);; s4 := (83,84);; 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,
s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s1*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1,
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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(84)!(1,2); s1 := Sym(84)!(23,28)(24,29)(25,30)(26,31)(27,32)(33,38)(34,39)(35,40)(36,41)(37,42)(43,53)(44,54)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(51,61)(52,62)(63,78)(64,79)(65,80)(66,81)(67,82)(68,73)(69,74)(70,75)(71,76)(72,77); s2 := Sym(84)!( 3,43)( 4,47)( 5,46)( 6,45)( 7,44)( 8,48)( 9,52)(10,51)(11,50)(12,49)(13,53)(14,57)(15,56)(16,55)(17,54)(18,58)(19,62)(20,61)(21,60)(22,59)(23,63)(24,67)(25,66)(26,65)(27,64)(28,68)(29,72)(30,71)(31,70)(32,69)(33,73)(34,77)(35,76)(36,75)(37,74)(38,78)(39,82)(40,81)(41,80)(42,79); s3 := Sym(84)!( 3, 4)( 5, 7)( 8, 9)(10,12)(13,19)(14,18)(15,22)(16,21)(17,20)(23,24)(25,27)(28,29)(30,32)(33,39)(34,38)(35,42)(36,41)(37,40)(43,64)(44,63)(45,67)(46,66)(47,65)(48,69)(49,68)(50,72)(51,71)(52,70)(53,79)(54,78)(55,82)(56,81)(57,80)(58,74)(59,73)(60,77)(61,76)(62,75); s4 := Sym(84)!(83,84); poly := sub<Sym(84)|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, s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s1*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1, 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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;