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