Overview
- Group
- SmallGroup(1920,150684)
- Rank
- 5
- Schläfli Type
- {3,2,4,40}
- Vertices, edges, …
- 3, 3, 4, 80, 40
- Order of s0s1s2s3s4
- 120
- 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 := (2,3);; s1 := (1,2);; s2 := (24,29)(25,30)(26,31)(27,32)(28,33)(34,39)(35,40)(36,41)(37,42)(38,43)(44,54)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(51,61)(52,62)(53,63)(64,79)(65,80)(66,81)(67,82)(68,83)(69,74)(70,75)(71,76)(72,77)(73,78);; s3 := ( 4,44)( 5,48)( 6,47)( 7,46)( 8,45)( 9,49)(10,53)(11,52)(12,51)(13,50)(14,54)(15,58)(16,57)(17,56)(18,55)(19,59)(20,63)(21,62)(22,61)(23,60)(24,69)(25,73)(26,72)(27,71)(28,70)(29,64)(30,68)(31,67)(32,66)(33,65)(34,79)(35,83)(36,82)(37,81)(38,80)(39,74)(40,78)(41,77)(42,76)(43,75);; s4 := ( 4, 5)( 6, 8)( 9,10)(11,13)(14,20)(15,19)(16,23)(17,22)(18,21)(24,25)(26,28)(29,30)(31,33)(34,40)(35,39)(36,43)(37,42)(38,41)(44,80)(45,79)(46,83)(47,82)(48,81)(49,75)(50,74)(51,78)(52,77)(53,76)(54,65)(55,64)(56,68)(57,67)(58,66)(59,70)(60,69)(61,73)(62,72)(63,71);; 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*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,
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s2*s3*s4*s3*s2*s3*s2*s4*s3*s4*s3*s2,
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*s3*s4*s2*s3*s4*s3*s2*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(83)!(2,3); s1 := Sym(83)!(1,2); s2 := Sym(83)!(24,29)(25,30)(26,31)(27,32)(28,33)(34,39)(35,40)(36,41)(37,42)(38,43)(44,54)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(51,61)(52,62)(53,63)(64,79)(65,80)(66,81)(67,82)(68,83)(69,74)(70,75)(71,76)(72,77)(73,78); s3 := Sym(83)!( 4,44)( 5,48)( 6,47)( 7,46)( 8,45)( 9,49)(10,53)(11,52)(12,51)(13,50)(14,54)(15,58)(16,57)(17,56)(18,55)(19,59)(20,63)(21,62)(22,61)(23,60)(24,69)(25,73)(26,72)(27,71)(28,70)(29,64)(30,68)(31,67)(32,66)(33,65)(34,79)(35,83)(36,82)(37,81)(38,80)(39,74)(40,78)(41,77)(42,76)(43,75); s4 := Sym(83)!( 4, 5)( 6, 8)( 9,10)(11,13)(14,20)(15,19)(16,23)(17,22)(18,21)(24,25)(26,28)(29,30)(31,33)(34,40)(35,39)(36,43)(37,42)(38,41)(44,80)(45,79)(46,83)(47,82)(48,81)(49,75)(50,74)(51,78)(52,77)(53,76)(54,65)(55,64)(56,68)(57,67)(58,66)(59,70)(60,69)(61,73)(62,72)(63,71); poly := sub<Sym(83)|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*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, s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3, s3*s4*s2*s3*s4*s3*s2*s3*s2*s4*s3*s4*s3*s2, 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*s3*s4*s2*s3*s4*s3*s2*s4*s3*s4 >;