Overview
- Group
- SmallGroup(1728,46139)
- Rank
- 6
- Schläfli Type
- {2,2,12,4,2}
- Vertices, edges, …
- 2, 2, 27, 54, 9, 2
- Order of s0s1s2s3s4s5
- 6
- Order of s0s1s2s3s4s5s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
3-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)(15,16)(17,20)(18,22)(19,21);; s3 := ( 5,15)( 6,14)( 7,16)( 8,18)( 9,17)(10,19)(11,21)(12,20)(13,22);; s4 := ( 5, 8)( 6,10)( 7, 9)(12,13)(15,16)(17,18)(20,22);; s5 := (23,24);; poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
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, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s4*s5*s4*s5, s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3*s2*s3*s4*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(24)!(1,2); s1 := Sym(24)!(3,4); s2 := Sym(24)!( 6, 7)( 9,10)(12,13)(15,16)(17,20)(18,22)(19,21); s3 := Sym(24)!( 5,15)( 6,14)( 7,16)( 8,18)( 9,17)(10,19)(11,21)(12,20)(13,22); s4 := Sym(24)!( 5, 8)( 6,10)( 7, 9)(12,13)(15,16)(17,18)(20,22); s5 := Sym(24)!(23,24); poly := sub<Sym(24)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 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, s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3*s2*s3*s4*s2*s3 >;