Overview
- Group
- SmallGroup(1920,240993)
- Rank
- 3
- Schläfli Type
- {6,6}
- Vertices, edges, …
- 160, 480, 160
- Order of s0s1s2
- 6
- Order of s0s1s2s1
- 5
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Non-Orientable
- Self-Dual
- Self-Petrie
Quotients maximal quotients in bold
16-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=<s1*s2*s1*s0*(s1*s2)^2*s1*s0*s2*s1*s2> of order 2
80 facets
- 80 of {6}*12
80 vertex figures
- 80 of {6}*12
P/N, where N=<s1*s2*s1*s0*(s1*s2)^2*s1*s0*s2*s1*s2, s0*(s2*(s1*s0)^2)^2*(s1*s2)^2> of order 4
40 facets
- 40 of {6}*12
40 vertex figures
- 40 of {6}*12
P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*s1*s2*s1*s0*s1, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s2*s1*s2> of order 4
40 facets
- 40 of {6}*12
40 vertex figures
- 40 of {6}*12
P/N, where N=<s1*s2*s1*s0*(s1*s2)^2*s1*s0*s2*s1*s2, s0*s1*s2*s1*s0*(s1*s2)^2*(s1*s0*s2)^2> of order 4
40 facets
- 40 of {6}*12
40 vertex figures
- 40 of {6}*12
P/N, where N=<s1*s2*s1*s0*(s1*s2)^2*s1*s0*s2*s1*s2, s0*(s2*(s1*s0)^2)^2*(s1*s2)^2*s1> of order 4
40 facets
- 40 of {6}*12
40 vertex figures
- 40 of {6}*12
P/N, where N=<s1*s2*s1*s0*(s1*s2)^2*s1*s0*s2*s1*s2, (s0*s1)^2*s2*s1*s0*s2*(s1*s0)^2*s2*s1> of order 4
40 facets
- 40 of {6}*12
40 vertex figures
- 40 of {6}*12
P/N, where N=<(s0*s1)^2*s0*s2*(s1*s0)^2*s1*s2*s1, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s2*s1*s2, s0*s1*s2*s1*s0*(s1*s2)^2*(s1*s0*s2)^2> of order 8
20 facets
- 20 of {6}*12
20 vertex figures
- 20 of {6}*12
P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*s1*s2*s1*s0*s1, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s2*s1*s2, (s0*s1)^2*(s2*s1)^2*(s0*s1)^2*s2*s1*s2> of order 8
20 facets
- 20 of {6}*12
20 vertex figures
- 20 of {6}*12
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*(s1*s2)^2*s1, (s0*s1)^2*s2*s1*s0*s2*(s1*s0)^2*s2*s1> of order 8
20 facets
- 20 of {6}*12
20 vertex figures
- 20 of {6}*12
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*(s1*s2)^2*s1, s0*s1*s0*(s2*s1)^2*s0*s1*s2*s1*s0*s1> of order 16
10 facets
- 10 of {6}*12
10 vertex figures
- 10 of {6}*12
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 4, 6)( 7,15)( 8,11)(10,13)(12,14);; s1 := ( 3, 8)( 4, 7)( 5,10)( 6, 9)(11,12)(15,16);; s2 := ( 1, 9)( 2, 7)( 3,15)( 4, 6)( 5,16)(12,14);; 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*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2,
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2,
s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(16)!( 2, 3)( 4, 6)( 7,15)( 8,11)(10,13)(12,14); s1 := Sym(16)!( 3, 8)( 4, 7)( 5,10)( 6, 9)(11,12)(15,16); s2 := Sym(16)!( 1, 9)( 2, 7)( 3,15)( 4, 6)( 5,16)(12,14); 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*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2, s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2, s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1 >;
References
None.
to this polytope.