Overview
- Group
- SmallGroup(384,12882)
- Rank
- 4
- Schläfli Type
- {4,4,6}
- Vertices, edges, …
- 8, 16, 24, 6
- Order of s0s1s2s3
- 12
- Order of s0s1s2s3s2s1
- 2
- Also known as
- {{4,4}4,{4,6|2}}. if this polytope has another name.
Special Properties
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
8-fold
12-fold
16-fold
24-fold
Covers minimal covers in bold
2-fold
3-fold
5-fold
Irregular Quotients of which this is a minimal cover
Click an entry to reveal its facets and vertex figures.
P/N, where N=<(s1*s2)^2> of order 2
6 facets
- 6 of 2-fold non-regular quotient of {4,4}*64
6 vertex figures
Representations
Permutation Representation (GAP)
s0 := ( 1,13)( 2,14)( 3,15)( 4,16)( 5,17)( 6,18)( 7,19)( 8,20)( 9,21)(10,22)(11,23)(12,24);; s1 := (19,22)(20,23)(21,24);; s2 := ( 1, 7)( 2, 9)( 3, 8)( 4,10)( 5,12)( 6,11)(13,19)(14,21)(15,20)(16,22)(17,24)(18,23);; s3 := ( 1, 2)( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23);; 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*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(24)!( 1,13)( 2,14)( 3,15)( 4,16)( 5,17)( 6,18)( 7,19)( 8,20)( 9,21)(10,22)(11,23)(12,24); s1 := Sym(24)!(19,22)(20,23)(21,24); s2 := Sym(24)!( 1, 7)( 2, 9)( 3, 8)( 4,10)( 5,12)( 6,11)(13,19)(14,21)(15,20)(16,22)(17,24)(18,23); s3 := Sym(24)!( 1, 2)( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23); 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*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References
None.
to this polytope.