Overview
- Group
- SmallGroup(1280,1036172)
- Rank
- 5
- Schläfli Type
- {2,2,4,40}
- Vertices, edges, …
- 2, 2, 4, 80, 40
- 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 := (25,30)(26,31)(27,32)(28,33)(29,34)(35,40)(36,41)(37,42)(38,43)(39,44)(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)(15,55)(16,59)(17,58)(18,57)(19,56)(20,60)(21,64)(22,63)(23,62)(24,61)(25,70)(26,74)(27,73)(28,72)(29,71)(30,65)(31,69)(32,68)(33,67)(34,66)(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)(45,81)(46,80)(47,84)(48,83)(49,82)(50,76)(51,75)(52,79)(53,78)(54,77)(55,66)(56,65)(57,69)(58,68)(59,67)(60,71)(61,70)(62,74)(63,73)(64,72);; 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*s2*s3*s2*s3*s2*s3,
s3*s4*s2*s3*s4*s3*s2*s3*s2*s4*s3*s4*s3*s2,
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*s2*s3*s4*s3*s2*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(84)!(1,2); s1 := Sym(84)!(3,4); s2 := Sym(84)!(25,30)(26,31)(27,32)(28,33)(29,34)(35,40)(36,41)(37,42)(38,43)(39,44)(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)(15,55)(16,59)(17,58)(18,57)(19,56)(20,60)(21,64)(22,63)(23,62)(24,61)(25,70)(26,74)(27,73)(28,72)(29,71)(30,65)(31,69)(32,68)(33,67)(34,66)(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)(45,81)(46,80)(47,84)(48,83)(49,82)(50,76)(51,75)(52,79)(53,78)(54,77)(55,66)(56,65)(57,69)(58,68)(59,67)(60,71)(61,70)(62,74)(63,73)(64,72); 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*s2*s3*s2*s3*s2*s3, s3*s4*s2*s3*s4*s3*s2*s3*s2*s4*s3*s4*s3*s2, 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*s2*s3*s4*s3*s2*s4*s3*s4 >;