Overview
- Group
- SmallGroup(1728,46139)
- Rank
- 5
- Schläfli Type
- {6,12,2,2}
- Vertices, edges, …
- 18, 108, 36, 2, 2
- Order of s0s1s2s3s4
- 4
- 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 := ( 1,28)( 2,29)( 3,30)( 4,34)( 5,35)( 6,36)( 7,31)( 8,32)( 9,33)(10,46)(11,47)(12,48)(13,52)(14,53)(15,54)(16,49)(17,50)(18,51)(19,37)(20,38)(21,39)(22,43)(23,44)(24,45)(25,40)(26,41)(27,42);; s1 := ( 1,10)( 2,12)( 3,11)( 4,14)( 5,13)( 6,15)( 7,18)( 8,17)( 9,16)(20,21)(22,23)(25,27)(28,37)(29,39)(30,38)(31,41)(32,40)(33,42)(34,45)(35,44)(36,43)(47,48)(49,50)(52,54);; s2 := ( 1, 2)( 4,20)( 5,19)( 6,21)( 7,11)( 8,10)( 9,12)(13,27)(14,26)(15,25)(17,18)(23,24)(28,29)(31,47)(32,46)(33,48)(34,38)(35,37)(36,39)(40,54)(41,53)(42,52)(44,45)(50,51);; s3 := (55,56);; 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*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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(58)!( 1,28)( 2,29)( 3,30)( 4,34)( 5,35)( 6,36)( 7,31)( 8,32)( 9,33)(10,46)(11,47)(12,48)(13,52)(14,53)(15,54)(16,49)(17,50)(18,51)(19,37)(20,38)(21,39)(22,43)(23,44)(24,45)(25,40)(26,41)(27,42); s1 := Sym(58)!( 1,10)( 2,12)( 3,11)( 4,14)( 5,13)( 6,15)( 7,18)( 8,17)( 9,16)(20,21)(22,23)(25,27)(28,37)(29,39)(30,38)(31,41)(32,40)(33,42)(34,45)(35,44)(36,43)(47,48)(49,50)(52,54); s2 := Sym(58)!( 1, 2)( 4,20)( 5,19)( 6,21)( 7,11)( 8,10)( 9,12)(13,27)(14,26)(15,25)(17,18)(23,24)(28,29)(31,47)(32,46)(33,48)(34,38)(35,37)(36,39)(40,54)(41,53)(42,52)(44,45)(50,51); s3 := Sym(58)!(55,56); 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*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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1 >;