Overview
- Group
- SmallGroup(1280,1036171)
- Rank
- 5
- Schläfli Type
- {2,2,20,8}
- Vertices, edges, …
- 2, 2, 20, 80, 8
- 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 := (3,4);; s2 := ( 6, 9)( 7, 8)(11,14)(12,13)(15,20)(16,24)(17,23)(18,22)(19,21)(26,29)(27,28)(31,34)(32,33)(35,40)(36,44)(37,43)(38,42)(39,41)(45,65)(46,69)(47,68)(48,67)(49,66)(50,70)(51,74)(52,73)(53,72)(54,71)(55,80)(56,84)(57,83)(58,82)(59,81)(60,75)(61,79)(62,78)(63,77)(64,76);; s3 := ( 5,46)( 6,45)( 7,49)( 8,48)( 9,47)(10,51)(11,50)(12,54)(13,53)(14,52)(15,61)(16,60)(17,64)(18,63)(19,62)(20,56)(21,55)(22,59)(23,58)(24,57)(25,66)(26,65)(27,69)(28,68)(29,67)(30,71)(31,70)(32,74)(33,73)(34,72)(35,81)(36,80)(37,84)(38,83)(39,82)(40,76)(41,75)(42,79)(43,78)(44,77);; s4 := (15,20)(16,21)(17,22)(18,23)(19,24)(25,30)(26,31)(27,32)(28,33)(29,34)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(51,61)(52,62)(53,63)(54,64)(65,80)(66,81)(67,82)(68,83)(69,84)(70,75)(71,76)(72,77)(73,78)(74,79);; 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, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s2*s3*s4*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*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(84)!(1,2); s1 := Sym(84)!(3,4); s2 := Sym(84)!( 6, 9)( 7, 8)(11,14)(12,13)(15,20)(16,24)(17,23)(18,22)(19,21)(26,29)(27,28)(31,34)(32,33)(35,40)(36,44)(37,43)(38,42)(39,41)(45,65)(46,69)(47,68)(48,67)(49,66)(50,70)(51,74)(52,73)(53,72)(54,71)(55,80)(56,84)(57,83)(58,82)(59,81)(60,75)(61,79)(62,78)(63,77)(64,76); s3 := Sym(84)!( 5,46)( 6,45)( 7,49)( 8,48)( 9,47)(10,51)(11,50)(12,54)(13,53)(14,52)(15,61)(16,60)(17,64)(18,63)(19,62)(20,56)(21,55)(22,59)(23,58)(24,57)(25,66)(26,65)(27,69)(28,68)(29,67)(30,71)(31,70)(32,74)(33,73)(34,72)(35,81)(36,80)(37,84)(38,83)(39,82)(40,76)(41,75)(42,79)(43,78)(44,77); s4 := Sym(84)!(15,20)(16,21)(17,22)(18,23)(19,24)(25,30)(26,31)(27,32)(28,33)(29,34)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(51,61)(52,62)(53,63)(54,64)(65,80)(66,81)(67,82)(68,83)(69,84)(70,75)(71,76)(72,77)(73,78)(74,79); 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, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s2*s3*s4*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*s2*s3 >;