Overview
- Group
- SmallGroup(1280,1036172)
- Rank
- 5
- Schläfli Type
- {2,40,4,2}
- Vertices, edges, …
- 2, 40, 80, 4, 2
- Order of s0s1s2s3s4
- 40
- 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 := ( 4, 7)( 5, 6)( 9,12)(10,11)(13,18)(14,22)(15,21)(16,20)(17,19)(24,27)(25,26)(29,32)(30,31)(33,38)(34,42)(35,41)(36,40)(37,39)(43,78)(44,82)(45,81)(46,80)(47,79)(48,73)(49,77)(50,76)(51,75)(52,74)(53,63)(54,67)(55,66)(56,65)(57,64)(58,68)(59,72)(60,71)(61,70)(62,69);; s2 := ( 3,44)( 4,43)( 5,47)( 6,46)( 7,45)( 8,49)( 9,48)(10,52)(11,51)(12,50)(13,54)(14,53)(15,57)(16,56)(17,55)(18,59)(19,58)(20,62)(21,61)(22,60)(23,69)(24,68)(25,72)(26,71)(27,70)(28,64)(29,63)(30,67)(31,66)(32,65)(33,79)(34,78)(35,82)(36,81)(37,80)(38,74)(39,73)(40,77)(41,76)(42,75);; s3 := (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);; 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, s2*s3*s2*s3*s2*s3*s2*s3,
s1*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*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*s3*s2*s1*s2*s1*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(84)!(1,2); s1 := Sym(84)!( 4, 7)( 5, 6)( 9,12)(10,11)(13,18)(14,22)(15,21)(16,20)(17,19)(24,27)(25,26)(29,32)(30,31)(33,38)(34,42)(35,41)(36,40)(37,39)(43,78)(44,82)(45,81)(46,80)(47,79)(48,73)(49,77)(50,76)(51,75)(52,74)(53,63)(54,67)(55,66)(56,65)(57,64)(58,68)(59,72)(60,71)(61,70)(62,69); s2 := Sym(84)!( 3,44)( 4,43)( 5,47)( 6,46)( 7,45)( 8,49)( 9,48)(10,52)(11,51)(12,50)(13,54)(14,53)(15,57)(16,56)(17,55)(18,59)(19,58)(20,62)(21,61)(22,60)(23,69)(24,68)(25,72)(26,71)(27,70)(28,64)(29,63)(30,67)(31,66)(32,65)(33,79)(34,78)(35,82)(36,81)(37,80)(38,74)(39,73)(40,77)(41,76)(42,75); s3 := 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); 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, s2*s3*s2*s3*s2*s3*s2*s3, s1*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*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*s3*s2*s1*s2*s1*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;