Overview
- Group
- SmallGroup(1728,47887)
- Rank
- 5
- Schläfli Type
- {4,4,6,2}
- Vertices, edges, …
- 18, 36, 54, 6, 2
- Order of s0s1s2s3s4
- 6
- 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
18-fold
36-fold
54-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 4,10)( 5,11)( 6,12)( 7,19)( 8,20)( 9,21)(16,22)(17,23)(18,24)(31,37)(32,38)(33,39)(34,46)(35,47)(36,48)(43,49)(44,50)(45,51);; s1 := (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);; s2 := ( 1,13)( 2,15)( 3,14)( 5, 6)( 7,22)( 8,24)( 9,23)(11,12)(16,19)(17,21)(18,20)(26,27)(28,40)(29,42)(30,41)(32,33)(34,49)(35,51)(36,50)(38,39)(43,46)(44,48)(45,47)(53,54);; s3 := ( 1,29)( 2,28)( 3,30)( 4,32)( 5,31)( 6,33)( 7,35)( 8,34)( 9,36)(10,38)(11,37)(12,39)(13,41)(14,40)(15,42)(16,44)(17,43)(18,45)(19,47)(20,46)(21,48)(22,50)(23,49)(24,51)(25,53)(26,52)(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*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(56)!( 4,10)( 5,11)( 6,12)( 7,19)( 8,20)( 9,21)(16,22)(17,23)(18,24)(31,37)(32,38)(33,39)(34,46)(35,47)(36,48)(43,49)(44,50)(45,51); s1 := 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); s2 := Sym(56)!( 1,13)( 2,15)( 3,14)( 5, 6)( 7,22)( 8,24)( 9,23)(11,12)(16,19)(17,21)(18,20)(26,27)(28,40)(29,42)(30,41)(32,33)(34,49)(35,51)(36,50)(38,39)(43,46)(44,48)(45,47)(53,54); s3 := Sym(56)!( 1,29)( 2,28)( 3,30)( 4,32)( 5,31)( 6,33)( 7,35)( 8,34)( 9,36)(10,38)(11,37)(12,39)(13,41)(14,40)(15,42)(16,44)(17,43)(18,45)(19,47)(20,46)(21,48)(22,50)(23,49)(24,51)(25,53)(26,52)(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*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;