Overview
- Group
- SmallGroup(1728,47887)
- Rank
- 5
- Schläfli Type
- {2,6,6,4}
- Vertices, edges, …
- 2, 6, 54, 36, 12
- 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
3-fold
6-fold
9-fold
18-fold
27-fold
36-fold
54-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)(34,35)(37,38)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56);; s2 := ( 3,31)( 4,30)( 5,32)( 6,37)( 7,36)( 8,38)( 9,34)(10,33)(11,35)(12,49)(13,48)(14,50)(15,55)(16,54)(17,56)(18,52)(19,51)(20,53)(21,40)(22,39)(23,41)(24,46)(25,45)(26,47)(27,43)(28,42)(29,44);; s3 := ( 3,12)( 4,13)( 5,14)( 6,15)( 7,16)( 8,17)( 9,18)(10,19)(11,20)(30,39)(31,40)(32,41)(33,42)(34,43)(35,44)(36,45)(37,46)(38,47);; s4 := ( 6,12)( 7,13)( 8,14)( 9,21)(10,22)(11,23)(18,24)(19,25)(20,26)(33,39)(34,40)(35,41)(36,48)(37,49)(38,50)(45,51)(46,52)(47,53);; 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,
s1*s2*s3*s2*s1*s2*s3*s2, s3*s4*s3*s4*s3*s4*s3*s4,
s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(56)!(1,2); s1 := Sym(56)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)(34,35)(37,38)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56); s2 := Sym(56)!( 3,31)( 4,30)( 5,32)( 6,37)( 7,36)( 8,38)( 9,34)(10,33)(11,35)(12,49)(13,48)(14,50)(15,55)(16,54)(17,56)(18,52)(19,51)(20,53)(21,40)(22,39)(23,41)(24,46)(25,45)(26,47)(27,43)(28,42)(29,44); s3 := Sym(56)!( 3,12)( 4,13)( 5,14)( 6,15)( 7,16)( 8,17)( 9,18)(10,19)(11,20)(30,39)(31,40)(32,41)(33,42)(34,43)(35,44)(36,45)(37,46)(38,47); s4 := Sym(56)!( 6,12)( 7,13)( 8,14)( 9,21)(10,22)(11,23)(18,24)(19,25)(20,26)(33,39)(34,40)(35,41)(36,48)(37,49)(38,50)(45,51)(46,52)(47,53); poly := sub<Sym(56)|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, s1*s2*s3*s2*s1*s2*s3*s2, s3*s4*s3*s4*s3*s4*s3*s4, s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;