Overview
- Group
- SmallGroup(1728,46139)
- Rank
- 5
- Schläfli Type
- {2,2,4,6}
- Vertices, edges, …
- 2, 2, 36, 108, 54
- 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
27-fold
54-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := (3,4);; s2 := ( 6, 7)( 9,10)(12,13)(14,23)(15,25)(16,24)(17,26)(18,28)(19,27)(20,29)(21,31)(22,30)(33,34)(36,37)(39,40)(41,50)(42,52)(43,51)(44,53)(45,55)(46,54)(47,56)(48,58)(49,57);; s3 := ( 6, 7)( 8,14)( 9,16)(10,15)(11,23)(12,25)(13,24)(17,18)(20,28)(21,27)(22,26)(29,30)(33,34)(35,41)(36,43)(37,42)(38,50)(39,52)(40,51)(44,45)(47,55)(48,54)(49,53)(56,57);; s4 := ( 5,35)( 6,36)( 7,37)( 8,32)( 9,33)(10,34)(11,38)(12,39)(13,40)(14,53)(15,54)(16,55)(17,50)(18,51)(19,52)(20,56)(21,57)(22,58)(23,44)(24,45)(25,46)(26,41)(27,42)(28,43)(29,47)(30,48)(31,49);; 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, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s4*s3*s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3*s4*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(58)!(1,2); s1 := Sym(58)!(3,4); s2 := Sym(58)!( 6, 7)( 9,10)(12,13)(14,23)(15,25)(16,24)(17,26)(18,28)(19,27)(20,29)(21,31)(22,30)(33,34)(36,37)(39,40)(41,50)(42,52)(43,51)(44,53)(45,55)(46,54)(47,56)(48,58)(49,57); s3 := Sym(58)!( 6, 7)( 8,14)( 9,16)(10,15)(11,23)(12,25)(13,24)(17,18)(20,28)(21,27)(22,26)(29,30)(33,34)(35,41)(36,43)(37,42)(38,50)(39,52)(40,51)(44,45)(47,55)(48,54)(49,53)(56,57); s4 := Sym(58)!( 5,35)( 6,36)( 7,37)( 8,32)( 9,33)(10,34)(11,38)(12,39)(13,40)(14,53)(15,54)(16,55)(17,50)(18,51)(19,52)(20,56)(21,57)(22,58)(23,44)(24,45)(25,46)(26,41)(27,42)(28,43)(29,47)(30,48)(31,49); 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, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s4*s3*s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3*s4*s3 >;