Overview
- Group
- SmallGroup(1344,11684)
- Rank
- 3
- Schläfli Type
- {6,4}
- Vertices, edges, …
- 168, 336, 112
- Order of s0s1s2
- 8
- Order of s0s1s2s1
- 8
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
2-fold
4-fold
168-fold
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=<(s2*s1*s0)^2*s1*(s2*s1*s0)^2*s2*s1*s2> of order 2
56 facets
- 56 of {6}*12
88 vertex figures
P/N, where N=<s1*s0*(s2*s1*s0*s1)^2*s2*s1*s0*s2*s1*s2> of order 2
56 facets
- 56 of {6}*12
84 vertex figures
- 84 of {4}*8
P/N, where N=<s1*s0*(s1*s2*(s1*s0)^2)^2*s1*s2*s1> of order 2
56 facets
- 56 of {6}*12
84 vertex figures
- 84 of {4}*8
P/N, where N=<s1*s0*(s1*(s2*s1*s0)^2)^2*(s1*s2)^2> of order 2
58 facets
84 vertex figures
- 84 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, s2*(s1*s0)^2*s1*(s2*s1*s0)^2*s1*s2> of order 4
28 facets
- 28 of {6}*12
48 vertex figures
P/N, where N=<s0*s1*s2*(s1*s0)^2*s2*s1*s0*s1*s2*s1> of order 4
28 facets
- 28 of {6}*12
44 vertex figures
P/N, where N=<s1*s0*s1*s2*(s1*s0)^2*s2*s1*s0*(s1*s2)^2> of order 4
28 facets
- 28 of {6}*12
44 vertex figures
P/N, where N=<s0*s1*s2*(s1*s0)^2*s1*s2*s1*s0*s1*s2*s1, (s1*s0)^2*(s1*s2*s1*s0)^2*s1*s2> of order 4
28 facets
- 28 of {6}*12
44 vertex figures
P/N, where N=<s0*s2*(s1*s0)^2*s1*s2, s1*s0*s2*s1*s0*s1*(s2*s1*s0)^2*s2*s1> of order 4
30 facets
44 vertex figures
P/N, where N=<s1*s0*s2*s1*s0*s1*(s2*s1*s0)^2*s2*s1, (s0*s1)^2*s2*s1*s0*s1*(s2*s1*s0)^2*s2*s1*s2> of order 4
28 facets
- 28 of {6}*12
44 vertex figures
P/N, where N=<((s1*s0)^2*s1*s2)^2, s1*s0*s1*s2*s1*s0*s1*(s2*s1*s0)^2*s2*s1*s2> of order 6
20 facets
28 vertex figures
- 28 of {4}*8
P/N, where N=<((s1*s0)^2*s1*s2)^2, s1*s0*s2*s1*s0*s1*(s2*s1*s0)^2*s2*s1> of order 6
20 facets
32 vertex figures
P/N, where N=<((s1*s0)^2*s1*s2)^2, (s0*s1)^2*s2*s1*s0*s1*(s2*s1*s0)^2*s2*s1*s2> of order 6
20 facets
28 vertex figures
- 28 of {4}*8
P/N, where N=<(s0*s1)^2*(s2*s1*s0*s1)^2> of order 7
16 facets
- 16 of {6}*12
24 vertex figures
- 24 of {4}*8
P/N, where N=<s0*s2*(s1*s0)^2*s1*s2, s0*s1*s0*s2*(s1*s0)^2*s2*s1*s0*s2*s1> of order 8
15 facets
22 vertex figures
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, s2*s1*s0*s1*s2*s1*s0*s2*s1*s2, ((s1*s0)^2*s1*s2)^2> of order 12
12 facets
16 vertex figures
P/N, where N=<(s0*s1)^2*(s2*s1*s0*s1)^2, s0*s1*s0*s2*(s1*s0)^2*s2*s1*s0*s1*s2> of order 14
8 facets
- 8 of {6}*12
12 vertex figures
- 12 of {4}*8
P/N, where N=<s1*s0*s2*(s1*s0)^2*s1*s2*s1, (s0*s1)^2*(s2*s1*s0*s1)^2> of order 14
10 facets
12 vertex figures
- 12 of {4}*8
Representations
Permutation Representation (GAP)
s0 := (3,8)(4,7)(5,6);; s1 := ( 1, 3)( 2, 6)( 4, 7)( 5, 8)( 9,10)(11,12);; s2 := ( 1, 2)( 3, 7)( 4, 8)( 5, 6)( 9,11)(10,12);; 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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(12)!(3,8)(4,7)(5,6); s1 := Sym(12)!( 1, 3)( 2, 6)( 4, 7)( 5, 8)( 9,10)(11,12); s2 := Sym(12)!( 1, 2)( 3, 7)( 4, 8)( 5, 6)( 9,11)(10,12); poly := sub<Sym(12)|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, s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1 >;
References
None.
to this polytope.