Overview
- Group
- SmallGroup(1120,1088)
- Rank
- 5
- Schläfli Type
- {2,2,10,14}
- Vertices, edges, …
- 2, 2, 10, 70, 14
- Order of s0s1s2s3s4
- 70
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
5-fold
7-fold
10-fold
14-fold
35-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := (3,4);; s2 := (12,33)(13,34)(14,35)(15,36)(16,37)(17,38)(18,39)(19,26)(20,27)(21,28)(22,29)(23,30)(24,31)(25,32)(47,68)(48,69)(49,70)(50,71)(51,72)(52,73)(53,74)(54,61)(55,62)(56,63)(57,64)(58,65)(59,66)(60,67);; s3 := ( 5,12)( 6,18)( 7,17)( 8,16)( 9,15)(10,14)(11,13)(19,33)(20,39)(21,38)(22,37)(23,36)(24,35)(25,34)(27,32)(28,31)(29,30)(40,47)(41,53)(42,52)(43,51)(44,50)(45,49)(46,48)(54,68)(55,74)(56,73)(57,72)(58,71)(59,70)(60,69)(62,67)(63,66)(64,65);; s4 := ( 5,41)( 6,40)( 7,46)( 8,45)( 9,44)(10,43)(11,42)(12,48)(13,47)(14,53)(15,52)(16,51)(17,50)(18,49)(19,55)(20,54)(21,60)(22,59)(23,58)(24,57)(25,56)(26,62)(27,61)(28,67)(29,66)(30,65)(31,64)(32,63)(33,69)(34,68)(35,74)(36,73)(37,72)(38,71)(39,70);; 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*s1*s0*s1,
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, 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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(74)!(1,2); s1 := Sym(74)!(3,4); s2 := Sym(74)!(12,33)(13,34)(14,35)(15,36)(16,37)(17,38)(18,39)(19,26)(20,27)(21,28)(22,29)(23,30)(24,31)(25,32)(47,68)(48,69)(49,70)(50,71)(51,72)(52,73)(53,74)(54,61)(55,62)(56,63)(57,64)(58,65)(59,66)(60,67); s3 := Sym(74)!( 5,12)( 6,18)( 7,17)( 8,16)( 9,15)(10,14)(11,13)(19,33)(20,39)(21,38)(22,37)(23,36)(24,35)(25,34)(27,32)(28,31)(29,30)(40,47)(41,53)(42,52)(43,51)(44,50)(45,49)(46,48)(54,68)(55,74)(56,73)(57,72)(58,71)(59,70)(60,69)(62,67)(63,66)(64,65); s4 := Sym(74)!( 5,41)( 6,40)( 7,46)( 8,45)( 9,44)(10,43)(11,42)(12,48)(13,47)(14,53)(15,52)(16,51)(17,50)(18,49)(19,55)(20,54)(21,60)(22,59)(23,58)(24,57)(25,56)(26,62)(27,61)(28,67)(29,66)(30,65)(31,64)(32,63)(33,69)(34,68)(35,74)(36,73)(37,72)(38,71)(39,70); poly := sub<Sym(74)|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*s1*s0*s1, 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, 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 >;