Overview
- Group
- SmallGroup(1728,46139)
- Rank
- 5
- Schläfli Type
- {2,12,6,2}
- Vertices, edges, …
- 2, 36, 108, 18, 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 := (1,2);; s1 := ( 4, 5)( 7, 8)(10,11)(12,21)(13,23)(14,22)(15,24)(16,26)(17,25)(18,27)(19,29)(20,28)(31,32)(34,35)(37,38)(39,48)(40,50)(41,49)(42,51)(43,53)(44,52)(45,54)(46,56)(47,55);; s2 := ( 3, 4)( 6,22)( 7,21)( 8,23)( 9,13)(10,12)(11,14)(15,29)(16,28)(17,27)(19,20)(25,26)(30,31)(33,49)(34,48)(35,50)(36,40)(37,39)(38,41)(42,56)(43,55)(44,54)(46,47)(52,53);; s3 := ( 3,33)( 4,34)( 5,35)( 6,30)( 7,31)( 8,32)( 9,36)(10,37)(11,38)(12,51)(13,52)(14,53)(15,48)(16,49)(17,50)(18,54)(19,55)(20,56)(21,42)(22,43)(23,44)(24,39)(25,40)(26,41)(27,45)(28,46)(29,47);; 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*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,
s3*s4*s3*s4, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(58)!(1,2); s1 := Sym(58)!( 4, 5)( 7, 8)(10,11)(12,21)(13,23)(14,22)(15,24)(16,26)(17,25)(18,27)(19,29)(20,28)(31,32)(34,35)(37,38)(39,48)(40,50)(41,49)(42,51)(43,53)(44,52)(45,54)(46,56)(47,55); s2 := Sym(58)!( 3, 4)( 6,22)( 7,21)( 8,23)( 9,13)(10,12)(11,14)(15,29)(16,28)(17,27)(19,20)(25,26)(30,31)(33,49)(34,48)(35,50)(36,40)(37,39)(38,41)(42,56)(43,55)(44,54)(46,47)(52,53); s3 := Sym(58)!( 3,33)( 4,34)( 5,35)( 6,30)( 7,31)( 8,32)( 9,36)(10,37)(11,38)(12,51)(13,52)(14,53)(15,48)(16,49)(17,50)(18,54)(19,55)(20,56)(21,42)(22,43)(23,44)(24,39)(25,40)(26,41)(27,45)(28,46)(29,47); 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*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, s3*s4*s3*s4, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2 >;