Overview
- Group
- SmallGroup(1280,1076043)
- Rank
- 5
- Schläfli Type
- {2,80,2,2}
- Vertices, edges, …
- 2, 80, 80, 2, 2
- 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 := ( 4, 7)( 5, 6)( 9,12)(10,11)(13,18)(14,22)(15,21)(16,20)(17,19)(23,33)(24,37)(25,36)(26,35)(27,34)(28,38)(29,42)(30,41)(31,40)(32,39)(43,63)(44,67)(45,66)(46,65)(47,64)(48,68)(49,72)(50,71)(51,70)(52,69)(53,78)(54,82)(55,81)(56,80)(57,79)(58,73)(59,77)(60,76)(61,75)(62,74);; s2 := ( 3,44)( 4,43)( 5,47)( 6,46)( 7,45)( 8,49)( 9,48)(10,52)(11,51)(12,50)(13,59)(14,58)(15,62)(16,61)(17,60)(18,54)(19,53)(20,57)(21,56)(22,55)(23,74)(24,73)(25,77)(26,76)(27,75)(28,79)(29,78)(30,82)(31,81)(32,80)(33,64)(34,63)(35,67)(36,66)(37,65)(38,69)(39,68)(40,72)(41,71)(42,70);; s3 := (83,84);; s4 := (85,86);; 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,
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4, 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*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*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*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*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*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*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(86)!(1,2); s1 := Sym(86)!( 4, 7)( 5, 6)( 9,12)(10,11)(13,18)(14,22)(15,21)(16,20)(17,19)(23,33)(24,37)(25,36)(26,35)(27,34)(28,38)(29,42)(30,41)(31,40)(32,39)(43,63)(44,67)(45,66)(46,65)(47,64)(48,68)(49,72)(50,71)(51,70)(52,69)(53,78)(54,82)(55,81)(56,80)(57,79)(58,73)(59,77)(60,76)(61,75)(62,74); s2 := Sym(86)!( 3,44)( 4,43)( 5,47)( 6,46)( 7,45)( 8,49)( 9,48)(10,52)(11,51)(12,50)(13,59)(14,58)(15,62)(16,61)(17,60)(18,54)(19,53)(20,57)(21,56)(22,55)(23,74)(24,73)(25,77)(26,76)(27,75)(28,79)(29,78)(30,82)(31,81)(32,80)(33,64)(34,63)(35,67)(36,66)(37,65)(38,69)(39,68)(40,72)(41,71)(42,70); s3 := Sym(86)!(83,84); s4 := Sym(86)!(85,86); poly := sub<Sym(86)|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, s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 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*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*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*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*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*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*s2*s1*s2*s1*s2 >;