Overview
- Group
- SmallGroup(1728,47887)
- Rank
- 5
- Schläfli Type
- {2,6,4,6}
- Vertices, edges, …
- 2, 6, 36, 36, 18
- 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
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, 4)( 6,13)( 7,12)( 8,14)( 9,22)(10,21)(11,23)(15,16)(18,25)(19,24)(20,26)(27,28)(30,31)(33,40)(34,39)(35,41)(36,49)(37,48)(38,50)(42,43)(45,52)(46,51)(47,53)(54,55);; s3 := (12,21)(13,22)(14,23)(15,24)(16,25)(17,26)(18,27)(19,28)(20,29)(39,48)(40,49)(41,50)(42,51)(43,52)(44,53)(45,54)(46,55)(47,56);; s4 := ( 3,42)( 4,43)( 5,44)( 6,39)( 7,40)( 8,41)( 9,45)(10,46)(11,47)(12,33)(13,34)(14,35)(15,30)(16,31)(17,32)(18,36)(19,37)(20,38)(21,51)(22,52)(23,53)(24,48)(25,49)(26,50)(27,54)(28,55)(29,56);; 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, s2*s3*s2*s3*s2*s3*s2*s3,
s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
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, 4)( 6,13)( 7,12)( 8,14)( 9,22)(10,21)(11,23)(15,16)(18,25)(19,24)(20,26)(27,28)(30,31)(33,40)(34,39)(35,41)(36,49)(37,48)(38,50)(42,43)(45,52)(46,51)(47,53)(54,55); s3 := Sym(56)!(12,21)(13,22)(14,23)(15,24)(16,25)(17,26)(18,27)(19,28)(20,29)(39,48)(40,49)(41,50)(42,51)(43,52)(44,53)(45,54)(46,55)(47,56); s4 := Sym(56)!( 3,42)( 4,43)( 5,44)( 6,39)( 7,40)( 8,41)( 9,45)(10,46)(11,47)(12,33)(13,34)(14,35)(15,30)(16,31)(17,32)(18,36)(19,37)(20,38)(21,51)(22,52)(23,53)(24,48)(25,49)(26,50)(27,54)(28,55)(29,56); 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, s2*s3*s2*s3*s2*s3*s2*s3, s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;