Overview
- Group
- SmallGroup(1792,1083341)
- Rank
- 6
- Schläfli Type
- {2,14,8,2,2}
- Vertices, edges, …
- 2, 14, 56, 8, 2, 2
- Order of s0s1s2s3s4s5
- 56
- Order of s0s1s2s3s4s5s4s3s2s1
- 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 := (1,2);; s1 := ( 4, 9)( 5, 8)( 6, 7)(11,16)(12,15)(13,14)(18,23)(19,22)(20,21)(25,30)(26,29)(27,28)(32,37)(33,36)(34,35)(39,44)(40,43)(41,42)(46,51)(47,50)(48,49)(53,58)(54,57)(55,56);; s2 := ( 3, 4)( 5, 9)( 6, 8)(10,11)(12,16)(13,15)(17,25)(18,24)(19,30)(20,29)(21,28)(22,27)(23,26)(31,46)(32,45)(33,51)(34,50)(35,49)(36,48)(37,47)(38,53)(39,52)(40,58)(41,57)(42,56)(43,55)(44,54);; s3 := ( 3,31)( 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)(17,52)(18,53)(19,54)(20,55)(21,56)(22,57)(23,58)(24,45)(25,46)(26,47)(27,48)(28,49)(29,50)(30,51);; s4 := (59,60);; s5 := (61,62);; poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s4*s5*s4*s5, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(62)!(1,2); s1 := Sym(62)!( 4, 9)( 5, 8)( 6, 7)(11,16)(12,15)(13,14)(18,23)(19,22)(20,21)(25,30)(26,29)(27,28)(32,37)(33,36)(34,35)(39,44)(40,43)(41,42)(46,51)(47,50)(48,49)(53,58)(54,57)(55,56); s2 := Sym(62)!( 3, 4)( 5, 9)( 6, 8)(10,11)(12,16)(13,15)(17,25)(18,24)(19,30)(20,29)(21,28)(22,27)(23,26)(31,46)(32,45)(33,51)(34,50)(35,49)(36,48)(37,47)(38,53)(39,52)(40,58)(41,57)(42,56)(43,55)(44,54); s3 := Sym(62)!( 3,31)( 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)(17,52)(18,53)(19,54)(20,55)(21,56)(22,57)(23,58)(24,45)(25,46)(26,47)(27,48)(28,49)(29,50)(30,51); s4 := Sym(62)!(59,60); s5 := Sym(62)!(61,62); poly := sub<Sym(62)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;