Overview
- Group
- SmallGroup(1152,157849)
- Rank
- 4
- Schläfli Type
- {4,6,4}
- Vertices, edges, …
- 16, 72, 72, 6
- Order of s0s1s2s3
- 4
- Order of s0s1s2s3s2s1
- 4
- Also known as
- if this polytope has a name.
Special Properties
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
No regular quotients.
Covers minimal covers in bold
None in this atlas.
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> of order 2
6 facets
- 6 of 2-fold non-regular quotient of {4,6}*192a
8 vertex figures
- 8 of {6,4}*72
P/N, where N=<(s0*s1)^2, s0*s2*s3*s2*s1*s0*s1*s2*s3*s2> of order 4
6 facets
- 6 of 4-fold non-regular quotient of {4,6}*192a
4 vertex figures
- 4 of {6,4}*72
Representations
Permutation Representation (GAP)
s0 := ( 1,11)( 2,12)( 3, 9)( 4,10)( 5,15)( 6,16)( 7,13)( 8,14);; s1 := ( 3, 4)( 5,13)( 6,14)( 7,16)( 8,15)(11,12);; s2 := ( 2, 5)( 3, 9)( 4,13)( 7,10)( 8,14)(12,15);; s3 := ( 5,13)( 6,14)( 7,15)( 8,16);; 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,
s2*s3*s2*s3*s2*s3*s2*s3, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2,
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(16)!( 1,11)( 2,12)( 3, 9)( 4,10)( 5,15)( 6,16)( 7,13)( 8,14); s1 := Sym(16)!( 3, 4)( 5,13)( 6,14)( 7,16)( 8,15)(11,12); s2 := Sym(16)!( 2, 5)( 3, 9)( 4,13)( 7,10)( 8,14)(12,15); s3 := Sym(16)!( 5,13)( 6,14)( 7,15)( 8,16); poly := sub<Sym(16)|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, s2*s3*s2*s3*s2*s3*s2*s3, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2, s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2 >;
References
None.
to this polytope.