Overview
- Group
- SmallGroup(1728,47912)
- Rank
- 5
- Schläfli Type
- {2,2,12,6}
- Vertices, edges, …
- 2, 2, 36, 108, 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 := (3,4);; s2 := ( 6, 7)( 8,14)( 9,16)(10,15)(11,23)(12,25)(13,24)(18,19)(20,26)(21,28)(22,27)(30,31)(33,34)(35,41)(36,43)(37,42)(38,50)(39,52)(40,51)(45,46)(47,53)(48,55)(49,54)(57,58);; s3 := ( 5, 6)( 8,12)( 9,11)(10,13)(14,15)(17,21)(18,20)(19,22)(23,24)(26,30)(27,29)(28,31)(32,33)(35,39)(36,38)(37,40)(41,42)(44,48)(45,47)(46,49)(50,51)(53,57)(54,56)(55,58);; s4 := ( 5,44)( 6,45)( 7,46)( 8,41)( 9,42)(10,43)(11,47)(12,48)(13,49)(14,35)(15,36)(16,37)(17,32)(18,33)(19,34)(20,38)(21,39)(22,40)(23,53)(24,54)(25,55)(26,50)(27,51)(28,52)(29,56)(30,57)(31,58);; 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, s1*s2*s1*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*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s3*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(58)!(1,2); s1 := Sym(58)!(3,4); s2 := Sym(58)!( 6, 7)( 8,14)( 9,16)(10,15)(11,23)(12,25)(13,24)(18,19)(20,26)(21,28)(22,27)(30,31)(33,34)(35,41)(36,43)(37,42)(38,50)(39,52)(40,51)(45,46)(47,53)(48,55)(49,54)(57,58); s3 := Sym(58)!( 5, 6)( 8,12)( 9,11)(10,13)(14,15)(17,21)(18,20)(19,22)(23,24)(26,30)(27,29)(28,31)(32,33)(35,39)(36,38)(37,40)(41,42)(44,48)(45,47)(46,49)(50,51)(53,57)(54,56)(55,58); s4 := Sym(58)!( 5,44)( 6,45)( 7,46)( 8,41)( 9,42)(10,43)(11,47)(12,48)(13,49)(14,35)(15,36)(16,37)(17,32)(18,33)(19,34)(20,38)(21,39)(22,40)(23,53)(24,54)(25,55)(26,50)(27,51)(28,52)(29,56)(30,57)(31,58); 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, s1*s2*s1*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*s4*s3*s4*s3*s4*s3*s4, s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s3*s2*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;