Overview
- Group
- SmallGroup(1280,323570)
- Rank
- 4
- Schläfli Type
- {2,4,40}
- Vertices, edges, …
- 2, 8, 160, 80
- Order of s0s1s2s3
- 20
- Order of s0s1s2s3s2s1
- 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
32-fold
40-fold
80-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 3,43)( 4,44)( 5,45)( 6,46)( 7,47)( 8,48)( 9,49)(10,50)(11,51)(12,52)(13,53)(14,54)(15,55)(16,56)(17,57)(18,58)(19,59)(20,60)(21,61)(22,62)(23,63)(24,64)(25,65)(26,66)(27,67)(28,68)(29,69)(30,70)(31,71)(32,72)(33,73)(34,74)(35,75)(36,76)(37,77)(38,78)(39,79)(40,80)(41,81)(42,82);; s2 := ( 4, 7)( 5, 6)( 9,12)(10,11)(13,18)(14,22)(15,21)(16,20)(17,19)(24,27)(25,26)(29,32)(30,31)(33,38)(34,42)(35,41)(36,40)(37,39)(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);; s3 := ( 3,44)( 4,43)( 5,47)( 6,46)( 7,45)( 8,49)( 9,48)(10,52)(11,51)(12,50)(13,54)(14,53)(15,57)(16,56)(17,55)(18,59)(19,58)(20,62)(21,61)(22,60)(23,79)(24,78)(25,82)(26,81)(27,80)(28,74)(29,73)(30,77)(31,76)(32,75)(33,69)(34,68)(35,72)(36,71)(37,70)(38,64)(39,63)(40,67)(41,66)(42,65);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(82)!(1,2); s1 := Sym(82)!( 3,43)( 4,44)( 5,45)( 6,46)( 7,47)( 8,48)( 9,49)(10,50)(11,51)(12,52)(13,53)(14,54)(15,55)(16,56)(17,57)(18,58)(19,59)(20,60)(21,61)(22,62)(23,63)(24,64)(25,65)(26,66)(27,67)(28,68)(29,69)(30,70)(31,71)(32,72)(33,73)(34,74)(35,75)(36,76)(37,77)(38,78)(39,79)(40,80)(41,81)(42,82); s2 := Sym(82)!( 4, 7)( 5, 6)( 9,12)(10,11)(13,18)(14,22)(15,21)(16,20)(17,19)(24,27)(25,26)(29,32)(30,31)(33,38)(34,42)(35,41)(36,40)(37,39)(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); s3 := Sym(82)!( 3,44)( 4,43)( 5,47)( 6,46)( 7,45)( 8,49)( 9,48)(10,52)(11,51)(12,50)(13,54)(14,53)(15,57)(16,56)(17,55)(18,59)(19,58)(20,62)(21,61)(22,60)(23,79)(24,78)(25,82)(26,81)(27,80)(28,74)(29,73)(30,77)(31,76)(32,75)(33,69)(34,68)(35,72)(36,71)(37,70)(38,64)(39,63)(40,67)(41,66)(42,65); poly := sub<Sym(82)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2, s2*s3*s2*s3*s2*s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3 >;