Overview
- Group
- SmallGroup(576,8654)
- Rank
- 4
- Schläfli Type
- {4,6,3}
- Vertices, edges, …
- 16, 48, 36, 3
- Order of s0s1s2s3
- 6
- Order of s0s1s2s3s2s1
- 4
- Also known as
- if this polytope has a name.
Special Properties
- Non-Orientable
- Flat
Quotients maximal quotients in bold
No regular quotients.
Covers minimal covers in bold
2-fold
3-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*s2*s1)^2*s0*(s1*s2)^2> of order 2
3 facets
- 1 of 2-fold non-regular quotient of {4,6}*192a
- 2 of 2-fold non-regular quotient of {4,6}*192a
8 vertex figures
- 8 of {6,3}*36
P/N, where N=<s0*s3*s2*s1*s0*s1*s2*s3, s0*s1*s0*s2*s1*s0*s1*s2*s1> of order 4
3 facets
- 1 of {4,6}*48c
- 2 of 4-fold non-regular quotient of {4,6}*192a
4 vertex figures
- 4 of {6,3}*36
P/N, where N=<(s0*s1)^2, (s0*s2*s1)^2*s0*(s1*s2)^2> of order 4
3 facets
- 3 of 4-fold non-regular quotient of {4,6}*192a
4 vertex figures
- 4 of {6,3}*36
Representations
Permutation Representation (GAP)
s0 := ( 1, 2)( 3, 4)( 5, 8)( 6, 7)( 9,11)(10,12);; s1 := ( 2, 3)( 7, 8)(10,12);; s2 := ( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11);; s3 := ( 1, 5)( 2, 8)( 3, 7)( 4, 6)(10,12);; 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*s3*s1*s2*s1*s2*s3*s1*s2,
s0*s1*s2*s1*s3*s0*s1*s2*s1*s3*s0*s1*s2*s1*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(12)!( 1, 2)( 3, 4)( 5, 8)( 6, 7)( 9,11)(10,12); s1 := Sym(12)!( 2, 3)( 7, 8)(10,12); s2 := Sym(12)!( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11); s3 := Sym(12)!( 1, 5)( 2, 8)( 3, 7)( 4, 6)(10,12); poly := sub<Sym(12)|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*s3*s1*s2*s1*s2*s3*s1*s2, s0*s1*s2*s1*s3*s0*s1*s2*s1*s3*s0*s1*s2*s1*s3 >;
References
None.
to this polytope.