Overview
- Group
- SmallGroup(1152,157478)
- Rank
- 4
- Schläfli Type
- {6,4,3}
- Vertices, edges, …
- 24, 96, 48, 12
- Order of s0s1s2s3
- 12
- Order of s0s1s2s3s2s1
- 4
- Also known as
- if this polytope has a name.
Special Properties
- Orientable
Quotients maximal quotients in bold
2-fold
32-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 5, 8)( 6, 7)(11,13)(12,14)(19,24)(20,23);; s1 := ( 1, 2)( 3, 7)( 4, 8)( 5, 6)( 9,10)(11,12)(13,15)(14,16)(17,18)(19,22)(20,21)(23,24);; s2 := ( 3, 4)( 9,22)(10,21)(11,20)(12,19)(13,23)(14,24)(15,18)(16,17);; s3 := ( 1,10)( 2, 9)( 3,16)( 4,15)( 5,11)( 6,12)( 7,14)( 8,13)(17,18);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s0*s1*s3*s2*s3*s1*s2*s0*s1*s3*s2*s3*s1*s2*s0*s1*s2*s3*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(24)!( 5, 8)( 6, 7)(11,13)(12,14)(19,24)(20,23); s1 := Sym(24)!( 1, 2)( 3, 7)( 4, 8)( 5, 6)( 9,10)(11,12)(13,15)(14,16)(17,18)(19,22)(20,21)(23,24); s2 := Sym(24)!( 3, 4)( 9,22)(10,21)(11,20)(12,19)(13,23)(14,24)(15,18)(16,17); s3 := Sym(24)!( 1,10)( 2, 9)( 3,16)( 4,15)( 5,11)( 6,12)( 7,14)( 8,13)(17,18); poly := sub<Sym(24)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, s2*s0*s1*s2*s0*s1*s3*s2*s3*s1*s2*s0*s1*s3*s2*s3*s1*s2*s0*s1*s2*s3*s0*s1 >;
References
None.
to this polytope.