Overview
- Group
- SmallGroup(1280,1076041)
- Rank
- 5
- Schläfli Type
- {2,2,10,16}
- Vertices, edges, …
- 2, 2, 10, 80, 16
- Order of s0s1s2s3s4
- 80
- 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)(16,19)(17,18)(21,24)(22,23)(26,29)(27,28)(31,34)(32,33)(36,39)(37,38)(41,44)(42,43)(46,49)(47,48)(51,54)(52,53)(56,59)(57,58)(61,64)(62,63)(66,69)(67,68)(71,74)(72,73)(76,79)(77,78)(81,84)(82,83);; s3 := ( 5, 6)( 7, 9)(10,11)(12,14)(15,21)(16,20)(17,24)(18,23)(19,22)(25,36)(26,35)(27,39)(28,38)(29,37)(30,41)(31,40)(32,44)(33,43)(34,42)(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);; s4 := ( 5,45)( 6,46)( 7,47)( 8,48)( 9,49)(10,50)(11,51)(12,52)(13,53)(14,54)(15,60)(16,61)(17,62)(18,63)(19,64)(20,55)(21,56)(22,57)(23,58)(24,59)(25,75)(26,76)(27,77)(28,78)(29,79)(30,80)(31,81)(32,82)(33,83)(34,84)(35,65)(36,66)(37,67)(38,68)(39,69)(40,70)(41,71)(42,72)(43,73)(44,74);; 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*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,
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)!( 6, 9)( 7, 8)(11,14)(12,13)(16,19)(17,18)(21,24)(22,23)(26,29)(27,28)(31,34)(32,33)(36,39)(37,38)(41,44)(42,43)(46,49)(47,48)(51,54)(52,53)(56,59)(57,58)(61,64)(62,63)(66,69)(67,68)(71,74)(72,73)(76,79)(77,78)(81,84)(82,83); s3 := Sym(84)!( 5, 6)( 7, 9)(10,11)(12,14)(15,21)(16,20)(17,24)(18,23)(19,22)(25,36)(26,35)(27,39)(28,38)(29,37)(30,41)(31,40)(32,44)(33,43)(34,42)(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); s4 := Sym(84)!( 5,45)( 6,46)( 7,47)( 8,48)( 9,49)(10,50)(11,51)(12,52)(13,53)(14,54)(15,60)(16,61)(17,62)(18,63)(19,64)(20,55)(21,56)(22,57)(23,58)(24,59)(25,75)(26,76)(27,77)(28,78)(29,79)(30,80)(31,81)(32,82)(33,83)(34,84)(35,65)(36,66)(37,67)(38,68)(39,69)(40,70)(41,71)(42,72)(43,73)(44,74); 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*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, 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 >;