Overview
- Group
- SmallGroup(256,6661)
- Rank
- 3
- Schläfli Type
- {4,8}
- Vertices, edges, …
- 16, 64, 32
- Order of s0s1s2
- 4
- Order of s0s1s2s1
- 8
- Also known as
- {4,8}4. if this polytope has another name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Self-Petrie
Quotients maximal quotients in bold
2-fold
4-fold
8-fold
16-fold
32-fold
Covers minimal covers in bold
2-fold
3-fold
5-fold
7-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)^4, s0*(s1*s2)^3*s1*s0*s1*s2*s1> of order 4
8 facets
- 8 of {4}*8
6 vertex figures
Representations
Permutation Representation (GAP)
s0 := ( 1, 9)( 2,10)( 3,11)( 4,12)( 5,13)( 6,14)( 7,15)( 8,16);; s1 := ( 5, 7)( 6, 8)(11,12)(13,14)(15,16);; s2 := ( 1,13)( 2,14)( 3,16)( 4,15)( 5, 9)( 6,10)( 7,12)( 8,11);; poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(16)!( 1, 9)( 2,10)( 3,11)( 4,12)( 5,13)( 6,14)( 7,15)( 8,16); s1 := Sym(16)!( 5, 7)( 6, 8)(11,12)(13,14)(15,16); s2 := Sym(16)!( 1,13)( 2,14)( 3,16)( 4,15)( 5, 9)( 6,10)( 7,12)( 8,11); poly := sub<Sym(16)|s0,s1,s2>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References
None.
to this polytope.