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