Overview
- Group
- SmallGroup(1920,240977)
- Rank
- 4
- Schläfli Type
- {2,8,6}
- Vertices, edges, …
- 2, 80, 240, 60
- 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
8-fold
120-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 3, 7)( 4,43)( 5,34)( 6,56)( 8,45)( 9,20)(11,16)(12,49)(13,18)(14,66)(15,46)(17,21)(19,64)(22,32)(23,55)(24,29)(25,38)(26,36)(27,31)(28,57)(30,41)(33,77)(35,80)(37,79)(39,78)(40,75)(44,82)(47,72)(48,63)(50,74)(51,68)(53,71)(54,81)(58,60)(59,62)(61,73)(65,69)(67,70);; s2 := ( 3,12)( 4,63)( 5,72)( 6,15)( 7, 8)( 9,43)(10,34)(11,56)(13,41)(14,37)(16,35)(17,44)(18,23)(19,39)(20,33)(21,40)(22,71)(24,52)(25,68)(26,74)(27,53)(28,60)(29,47)(30,61)(31,50)(32,45)(36,49)(38,48)(42,64)(46,55)(51,57)(54,66)(58,77)(59,79)(62,82)(65,75)(67,78)(69,81)(70,76)(73,80);; s3 := ( 3,15)( 4,18)( 5,74)( 6,69)( 7,46)( 8,24)( 9,32)(10,76)(11,57)(12,82)(13,43)(14,77)(16,28)(17,25)(19,75)(20,22)(21,38)(23,63)(26,51)(27,61)(29,45)(30,62)(31,73)(33,66)(34,50)(35,60)(36,68)(37,70)(39,72)(40,64)(41,59)(42,52)(44,49)(47,78)(48,55)(53,81)(54,71)(56,65)(58,80)(67,79);; 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,
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*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2,
s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(82)!(1,2); s1 := Sym(82)!( 3, 7)( 4,43)( 5,34)( 6,56)( 8,45)( 9,20)(11,16)(12,49)(13,18)(14,66)(15,46)(17,21)(19,64)(22,32)(23,55)(24,29)(25,38)(26,36)(27,31)(28,57)(30,41)(33,77)(35,80)(37,79)(39,78)(40,75)(44,82)(47,72)(48,63)(50,74)(51,68)(53,71)(54,81)(58,60)(59,62)(61,73)(65,69)(67,70); s2 := Sym(82)!( 3,12)( 4,63)( 5,72)( 6,15)( 7, 8)( 9,43)(10,34)(11,56)(13,41)(14,37)(16,35)(17,44)(18,23)(19,39)(20,33)(21,40)(22,71)(24,52)(25,68)(26,74)(27,53)(28,60)(29,47)(30,61)(31,50)(32,45)(36,49)(38,48)(42,64)(46,55)(51,57)(54,66)(58,77)(59,79)(62,82)(65,75)(67,78)(69,81)(70,76)(73,80); s3 := Sym(82)!( 3,15)( 4,18)( 5,74)( 6,69)( 7,46)( 8,24)( 9,32)(10,76)(11,57)(12,82)(13,43)(14,77)(16,28)(17,25)(19,75)(20,22)(21,38)(23,63)(26,51)(27,61)(29,45)(30,62)(31,73)(33,66)(34,50)(35,60)(36,68)(37,70)(39,72)(40,64)(41,59)(42,52)(44,49)(47,78)(48,55)(53,81)(54,71)(56,65)(58,80)(67,79); 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, 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*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2, s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1 >;