Overview
- Group
- SmallGroup(384,5602)
- Rank
- 4
- Schläfli Type
- {4,4,3}
- Vertices, edges, …
- 16, 32, 24, 3
- Order of s0s1s2s3
- 6
- Order of s0s1s2s3s2s1
- 4
- Also known as
- {{4,4|4},{4,3}3}. if this polytope has another name.
Special Properties
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
2-fold
8-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=<(s0*s1)^2*s2*s1*s0*s1*s2> of order 2
3 facets
- 3 of 2-fold non-regular quotient of {4,4}*128
8 vertex figures
- 8 of {4,3}*24
Representations
Permutation Representation (GAP)
s0 := (3,4)(5,6)(7,8);; s1 := (1,5)(2,6)(3,7)(4,8);; s2 := (3,5)(4,6);; s3 := (3,7)(4,8);; 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,
s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s3*s1*s2*s3*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(8)!(3,4)(5,6)(7,8); s1 := Sym(8)!(1,5)(2,6)(3,7)(4,8); s2 := Sym(8)!(3,5)(4,6); s3 := Sym(8)!(3,7)(4,8); poly := sub<Sym(8)|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, s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s1*s2*s3*s1*s2 >;
References
None.
to this polytope.