Overview
- Group
- SmallGroup(324,39)
- Rank
- 4
- Schläfli Type
- {3,6,3}
- Vertices, edges, …
- 9, 27, 27, 3
- Order of s0s1s2s3
- 9
- Order of s0s1s2s3s2s1
- 6
- Also known as
- 7T4(3,0)(1,1). if this polytope has another name.
Special Properties
- Universal
- Locally Toroidal
- Orientable
- Flat
Quotients maximal quotients in bold
3-fold
9-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
5-fold
6-fold
Irregular Quotients of which this is a minimal cover
Click an entry to reveal its facets and vertex figures.
Representations
Permutation Representation (GAP)
s0 := (1,7)(2,8)(3,9);; s1 := (4,7)(5,8)(6,9);; s2 := (2,3)(4,5)(8,9);; s3 := (2,3)(5,6)(8,9);; 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,
s2*s3*s2*s3*s2*s3, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(9)!(1,7)(2,8)(3,9); s1 := Sym(9)!(4,7)(5,8)(6,9); s2 := Sym(9)!(2,3)(4,5)(8,9); s3 := Sym(9)!(2,3)(5,6)(8,9); poly := sub<Sym(9)|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, s2*s3*s2*s3*s2*s3, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2 >;
References
- Theorem 11E7, McMullen P., Schulte, E.; Abstract Regular Polytopes (Cambridge University Press, 2002)
to this polytope.