Overview
- Group
- SmallGroup(1152,157478)
- Rank
- 4
- Schläfli Type
- {3,4,6}
- Vertices, edges, …
- 12, 48, 96, 24
- 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 := ( 3, 8)( 4, 7)(13,16)(14,15)(19,21)(20,22);; s2 := ( 3, 4)( 9,22)(10,21)(11,20)(12,19)(13,23)(14,24)(15,18)(16,17);; s3 := ( 1, 9)( 2,10)( 3,15)( 4,16)( 5,12)( 6,11)( 7,13)( 8,14)(19,20)(21,22)(23,24);; 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, s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s0*s2*s1*s2*s3*s2*s1*s0*s2*s1*s2*s3*s2*s1*s0*s2*s1*s2*s3*s1*s0 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(24)!( 5, 8)( 6, 7)(11,13)(12,14)(19,24)(20,23); s1 := Sym(24)!( 3, 8)( 4, 7)(13,16)(14,15)(19,21)(20,22); 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, 9)( 2,10)( 3,15)( 4,16)( 5,12)( 6,11)( 7,13)( 8,14)(19,20)(21,22)(23,24); 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, s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s0*s2*s1*s2*s3*s2*s1*s0*s2*s1*s2*s3*s2*s1*s0*s2*s1*s2*s3*s1*s0 >;
References
None.
to this polytope.