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