Overview
- Group
- SmallGroup(1920,203901)
- Rank
- 5
- Schläfli Type
- {3,2,10,16}
- Vertices, edges, …
- 3, 3, 10, 80, 16
- Order of s0s1s2s3s4
- 240
- 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)(15,18)(16,17)(20,23)(21,22)(25,28)(26,27)(30,33)(31,32)(35,38)(36,37)(40,43)(41,42)(45,48)(46,47)(50,53)(51,52)(55,58)(56,57)(60,63)(61,62)(65,68)(66,67)(70,73)(71,72)(75,78)(76,77)(80,83)(81,82);; s3 := ( 4, 5)( 6, 8)( 9,10)(11,13)(14,20)(15,19)(16,23)(17,22)(18,21)(24,35)(25,34)(26,38)(27,37)(28,36)(29,40)(30,39)(31,43)(32,42)(33,41)(44,65)(45,64)(46,68)(47,67)(48,66)(49,70)(50,69)(51,73)(52,72)(53,71)(54,80)(55,79)(56,83)(57,82)(58,81)(59,75)(60,74)(61,78)(62,77)(63,76);; s4 := ( 4,44)( 5,45)( 6,46)( 7,47)( 8,48)( 9,49)(10,50)(11,51)(12,52)(13,53)(14,59)(15,60)(16,61)(17,62)(18,63)(19,54)(20,55)(21,56)(22,57)(23,58)(24,74)(25,75)(26,76)(27,77)(28,78)(29,79)(30,80)(31,81)(32,82)(33,83)(34,64)(35,65)(36,66)(37,67)(38,68)(39,69)(40,70)(41,71)(42,72)(43,73);; 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*s4*s3*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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 ];;
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)(15,18)(16,17)(20,23)(21,22)(25,28)(26,27)(30,33)(31,32)(35,38)(36,37)(40,43)(41,42)(45,48)(46,47)(50,53)(51,52)(55,58)(56,57)(60,63)(61,62)(65,68)(66,67)(70,73)(71,72)(75,78)(76,77)(80,83)(81,82); s3 := Sym(83)!( 4, 5)( 6, 8)( 9,10)(11,13)(14,20)(15,19)(16,23)(17,22)(18,21)(24,35)(25,34)(26,38)(27,37)(28,36)(29,40)(30,39)(31,43)(32,42)(33,41)(44,65)(45,64)(46,68)(47,67)(48,66)(49,70)(50,69)(51,73)(52,72)(53,71)(54,80)(55,79)(56,83)(57,82)(58,81)(59,75)(60,74)(61,78)(62,77)(63,76); s4 := Sym(83)!( 4,44)( 5,45)( 6,46)( 7,47)( 8,48)( 9,49)(10,50)(11,51)(12,52)(13,53)(14,59)(15,60)(16,61)(17,62)(18,63)(19,54)(20,55)(21,56)(22,57)(23,58)(24,74)(25,75)(26,76)(27,77)(28,78)(29,79)(30,80)(31,81)(32,82)(33,83)(34,64)(35,65)(36,66)(37,67)(38,68)(39,69)(40,70)(41,71)(42,72)(43,73); 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*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 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 >;