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