Overview
- Group
- SmallGroup(1120,1088)
- Rank
- 5
- Schläfli Type
- {2,2,14,10}
- Vertices, edges, …
- 2, 2, 14, 70, 10
- 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 := ( 6,11)( 7,10)( 8, 9)(13,18)(14,17)(15,16)(20,25)(21,24)(22,23)(27,32)(28,31)(29,30)(34,39)(35,38)(36,37)(41,46)(42,45)(43,44)(48,53)(49,52)(50,51)(55,60)(56,59)(57,58)(62,67)(63,66)(64,65)(69,74)(70,73)(71,72);; s3 := ( 5, 6)( 7,11)( 8,10)(12,34)(13,33)(14,39)(15,38)(16,37)(17,36)(18,35)(19,27)(20,26)(21,32)(22,31)(23,30)(24,29)(25,28)(40,41)(42,46)(43,45)(47,69)(48,68)(49,74)(50,73)(51,72)(52,71)(53,70)(54,62)(55,61)(56,67)(57,66)(58,65)(59,64)(60,63);; s4 := ( 5,47)( 6,48)( 7,49)( 8,50)( 9,51)(10,52)(11,53)(12,40)(13,41)(14,42)(15,43)(16,44)(17,45)(18,46)(19,68)(20,69)(21,70)(22,71)(23,72)(24,73)(25,74)(26,61)(27,62)(28,63)(29,64)(30,65)(31,66)(32,67)(33,54)(34,55)(35,56)(36,57)(37,58)(38,59)(39,60);; 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,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
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*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(74)!(1,2); s1 := Sym(74)!(3,4); s2 := Sym(74)!( 6,11)( 7,10)( 8, 9)(13,18)(14,17)(15,16)(20,25)(21,24)(22,23)(27,32)(28,31)(29,30)(34,39)(35,38)(36,37)(41,46)(42,45)(43,44)(48,53)(49,52)(50,51)(55,60)(56,59)(57,58)(62,67)(63,66)(64,65)(69,74)(70,73)(71,72); s3 := Sym(74)!( 5, 6)( 7,11)( 8,10)(12,34)(13,33)(14,39)(15,38)(16,37)(17,36)(18,35)(19,27)(20,26)(21,32)(22,31)(23,30)(24,29)(25,28)(40,41)(42,46)(43,45)(47,69)(48,68)(49,74)(50,73)(51,72)(52,71)(53,70)(54,62)(55,61)(56,67)(57,66)(58,65)(59,64)(60,63); s4 := Sym(74)!( 5,47)( 6,48)( 7,49)( 8,50)( 9,51)(10,52)(11,53)(12,40)(13,41)(14,42)(15,43)(16,44)(17,45)(18,46)(19,68)(20,69)(21,70)(22,71)(23,72)(24,73)(25,74)(26,61)(27,62)(28,63)(29,64)(30,65)(31,66)(32,67)(33,54)(34,55)(35,56)(36,57)(37,58)(38,59)(39,60); 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, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 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*s3*s2*s3 >;