Overview
- Group
- SmallGroup(1344,8561)
- Rank
- 5
- Schläfli Type
- {3,2,14,8}
- Vertices, edges, …
- 3, 3, 14, 56, 8
- Order of s0s1s2s3s4
- 168
- 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
7-fold
8-fold
14-fold
28-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (2,3);; s1 := (1,2);; s2 := ( 5,10)( 6, 9)( 7, 8)(12,17)(13,16)(14,15)(19,24)(20,23)(21,22)(26,31)(27,30)(28,29)(33,38)(34,37)(35,36)(40,45)(41,44)(42,43)(47,52)(48,51)(49,50)(54,59)(55,58)(56,57);; s3 := ( 4, 5)( 6,10)( 7, 9)(11,12)(13,17)(14,16)(18,26)(19,25)(20,31)(21,30)(22,29)(23,28)(24,27)(32,47)(33,46)(34,52)(35,51)(36,50)(37,49)(38,48)(39,54)(40,53)(41,59)(42,58)(43,57)(44,56)(45,55);; s4 := ( 4,32)( 5,33)( 6,34)( 7,35)( 8,36)( 9,37)(10,38)(11,39)(12,40)(13,41)(14,42)(15,43)(16,44)(17,45)(18,53)(19,54)(20,55)(21,56)(22,57)(23,58)(24,59)(25,46)(26,47)(27,48)(28,49)(29,50)(30,51)(31,52);; 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,
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(59)!(2,3); s1 := Sym(59)!(1,2); s2 := Sym(59)!( 5,10)( 6, 9)( 7, 8)(12,17)(13,16)(14,15)(19,24)(20,23)(21,22)(26,31)(27,30)(28,29)(33,38)(34,37)(35,36)(40,45)(41,44)(42,43)(47,52)(48,51)(49,50)(54,59)(55,58)(56,57); s3 := Sym(59)!( 4, 5)( 6,10)( 7, 9)(11,12)(13,17)(14,16)(18,26)(19,25)(20,31)(21,30)(22,29)(23,28)(24,27)(32,47)(33,46)(34,52)(35,51)(36,50)(37,49)(38,48)(39,54)(40,53)(41,59)(42,58)(43,57)(44,56)(45,55); s4 := Sym(59)!( 4,32)( 5,33)( 6,34)( 7,35)( 8,36)( 9,37)(10,38)(11,39)(12,40)(13,41)(14,42)(15,43)(16,44)(17,45)(18,53)(19,54)(20,55)(21,56)(22,57)(23,58)(24,59)(25,46)(26,47)(27,48)(28,49)(29,50)(30,51)(31,52); poly := sub<Sym(59)|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, 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 >;