Overview
- Group
- SmallGroup(1728,46139)
- Rank
- 5
- Schläfli Type
- {2,6,12,2}
- Vertices, edges, …
- 2, 18, 108, 36, 2
- Order of s0s1s2s3s4
- 12
- 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
3-fold
6-fold
27-fold
54-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 3,30)( 4,31)( 5,32)( 6,36)( 7,37)( 8,38)( 9,33)(10,34)(11,35)(12,48)(13,49)(14,50)(15,54)(16,55)(17,56)(18,51)(19,52)(20,53)(21,39)(22,40)(23,41)(24,45)(25,46)(26,47)(27,42)(28,43)(29,44);; s2 := ( 3,12)( 4,14)( 5,13)( 6,16)( 7,15)( 8,17)( 9,20)(10,19)(11,18)(22,23)(24,25)(27,29)(30,39)(31,41)(32,40)(33,43)(34,42)(35,44)(36,47)(37,46)(38,45)(49,50)(51,52)(54,56);; s3 := ( 4, 5)( 6,12)( 7,14)( 8,13)( 9,21)(10,23)(11,22)(15,16)(18,26)(19,25)(20,24)(27,28)(31,32)(33,39)(34,41)(35,40)(36,48)(37,50)(38,49)(42,43)(45,53)(46,52)(47,51)(54,55);; s4 := (57,58);; 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, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s2*s3*s2*s3*s2*s1*s2*s1*s2*s3*s2*s3*s2,
s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(58)!(1,2); s1 := Sym(58)!( 3,30)( 4,31)( 5,32)( 6,36)( 7,37)( 8,38)( 9,33)(10,34)(11,35)(12,48)(13,49)(14,50)(15,54)(16,55)(17,56)(18,51)(19,52)(20,53)(21,39)(22,40)(23,41)(24,45)(25,46)(26,47)(27,42)(28,43)(29,44); s2 := Sym(58)!( 3,12)( 4,14)( 5,13)( 6,16)( 7,15)( 8,17)( 9,20)(10,19)(11,18)(22,23)(24,25)(27,29)(30,39)(31,41)(32,40)(33,43)(34,42)(35,44)(36,47)(37,46)(38,45)(49,50)(51,52)(54,56); s3 := Sym(58)!( 4, 5)( 6,12)( 7,14)( 8,13)( 9,21)(10,23)(11,22)(15,16)(18,26)(19,25)(20,24)(27,28)(31,32)(33,39)(34,41)(35,40)(36,48)(37,50)(38,49)(42,43)(45,53)(46,52)(47,51)(54,55); s4 := Sym(58)!(57,58); poly := sub<Sym(58)|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, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s1*s2*s3*s2*s3*s2*s1*s2*s1*s2*s3*s2*s3*s2, s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2 >;