Overview
- Group
- SmallGroup(1280,1076041)
- Rank
- 5
- Schläfli Type
- {2,16,10,2}
- Vertices, edges, …
- 2, 16, 80, 10, 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 := (13,18)(14,19)(15,20)(16,21)(17,22)(23,33)(24,34)(25,35)(26,36)(27,37)(28,38)(29,39)(30,40)(31,41)(32,42)(43,63)(44,64)(45,65)(46,66)(47,67)(48,68)(49,69)(50,70)(51,71)(52,72)(53,78)(54,79)(55,80)(56,81)(57,82)(58,73)(59,74)(60,75)(61,76)(62,77);; s2 := ( 3,43)( 4,47)( 5,46)( 6,45)( 7,44)( 8,48)( 9,52)(10,51)(11,50)(12,49)(13,58)(14,62)(15,61)(16,60)(17,59)(18,53)(19,57)(20,56)(21,55)(22,54)(23,73)(24,77)(25,76)(26,75)(27,74)(28,78)(29,82)(30,81)(31,80)(32,79)(33,63)(34,67)(35,66)(36,65)(37,64)(38,68)(39,72)(40,71)(41,70)(42,69);; s3 := ( 3, 4)( 5, 7)( 8, 9)(10,12)(13,14)(15,17)(18,19)(20,22)(23,24)(25,27)(28,29)(30,32)(33,34)(35,37)(38,39)(40,42)(43,44)(45,47)(48,49)(50,52)(53,54)(55,57)(58,59)(60,62)(63,64)(65,67)(68,69)(70,72)(73,74)(75,77)(78,79)(80,82);; s4 := (83,84);; 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,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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(84)!(1,2); s1 := Sym(84)!(13,18)(14,19)(15,20)(16,21)(17,22)(23,33)(24,34)(25,35)(26,36)(27,37)(28,38)(29,39)(30,40)(31,41)(32,42)(43,63)(44,64)(45,65)(46,66)(47,67)(48,68)(49,69)(50,70)(51,71)(52,72)(53,78)(54,79)(55,80)(56,81)(57,82)(58,73)(59,74)(60,75)(61,76)(62,77); s2 := Sym(84)!( 3,43)( 4,47)( 5,46)( 6,45)( 7,44)( 8,48)( 9,52)(10,51)(11,50)(12,49)(13,58)(14,62)(15,61)(16,60)(17,59)(18,53)(19,57)(20,56)(21,55)(22,54)(23,73)(24,77)(25,76)(26,75)(27,74)(28,78)(29,82)(30,81)(31,80)(32,79)(33,63)(34,67)(35,66)(36,65)(37,64)(38,68)(39,72)(40,71)(41,70)(42,69); s3 := Sym(84)!( 3, 4)( 5, 7)( 8, 9)(10,12)(13,14)(15,17)(18,19)(20,22)(23,24)(25,27)(28,29)(30,32)(33,34)(35,37)(38,39)(40,42)(43,44)(45,47)(48,49)(50,52)(53,54)(55,57)(58,59)(60,62)(63,64)(65,67)(68,69)(70,72)(73,74)(75,77)(78,79)(80,82); s4 := Sym(84)!(83,84); 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, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 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 >;