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