Overview
- Group
- SmallGroup(1152,157849)
- Rank
- 3
- Schläfli Type
- {4,6}
- Vertices, edges, …
- 96, 288, 144
- Order of s0s1s2
- 8
- Order of s0s1s2s1
- 6
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Non-Orientable
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=<s0*s1*s0*(s2*s1*s0*s1)^2*s2*s1> of order 2
72 facets
- 72 of {4}*8
48 vertex figures
- 48 of {6}*12
P/N, where N=<s0*s2*s1*(s0*(s2*s1)^2)^2*s0*s2*s1*s2> of order 2
72 facets
- 72 of {4}*8
48 vertex figures
- 48 of {6}*12
P/N, where N=<s0*s1*s0*(s2*s1*s0*s1)^2*s2*s1, (s1*s2)^2*s1*s0*s1*s2*s1*s0*(s2*s1)^2*s0*s1*s2> of order 4
36 facets
- 36 of {4}*8
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s0*s2*s1)^4, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s2*s1*s2> of order 4
36 facets
- 36 of {4}*8
24 vertex figures
- 24 of {6}*12
P/N, where N=<s0*s1*s0*(s2*s1*s0*s1)^2*s2*s1, s0*(s1*s2)^2*s1*s0*(s1*s2)^3> of order 4
36 facets
- 36 of {4}*8
24 vertex figures
- 24 of {6}*12
P/N, where N=<s0*s1*s0*(s2*s1*s0*s1)^2*s2> of order 4
36 facets
- 36 of {4}*8
24 vertex figures
- 24 of {6}*12
P/N, where N=<s0*s1*s0*(s2*s1*s0*s1)^2*s2*s1, (s0*s2*s1)^2*s0*s1*s2*s1*s0*(s1*s2)^2> of order 4
36 facets
- 36 of {4}*8
24 vertex figures
- 24 of {6}*12
P/N, where N=<s0*s1*s0*(s2*s1*s0*s1)^2*s2*s1, s0*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 4
36 facets
- 36 of {4}*8
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s0*s1)^2*(s2*s1*s0*s1)^2*s2, s0*s1*s0*(s2*s1*s0*s1)^2*s2*s1> of order 4
36 facets
- 36 of {4}*8
24 vertex figures
- 24 of {6}*12
P/N, where N=<s0*s1*s0*(s2*s1*s0*s1)^2*s2*s1, s1*s0*s1*(s2*s1*s0)^2*s1*s2*s1*s0*(s1*s2)^2> of order 4
36 facets
- 36 of {4}*8
24 vertex figures
- 24 of {6}*12
P/N, where N=<s0*(s1*s0*s2)^3*s1*s2, (s0*s2*s1)^4, s0*s1*s0*(s2*s1*s0*s1)^2*s2*s1> of order 8
18 facets
- 18 of {4}*8
12 vertex figures
- 12 of {6}*12
P/N, where N=<(s0*s1)^2*(s2*s1*s0*s1)^2*s2, s0*s1*s0*(s2*s1*s0*s1)^2*s2*s1, s0*(s1*s2)^2*s1*s0*(s1*s2)^3> of order 8
18 facets
- 18 of {4}*8
12 vertex figures
- 12 of {6}*12
P/N, where N=<s0*s1*s0*(s2*s1*s0*s1)^2*s2, (s0*s2*s1)^4> of order 8
18 facets
- 18 of {4}*8
12 vertex figures
- 12 of {6}*12
P/N, where N=<(s0*s1)^2*(s2*s1*s0*s1)^2*s2, s0*s1*s0*(s2*s1*s0*s1)^2*s2*s1, s0*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 8
18 facets
- 18 of {4}*8
12 vertex figures
- 12 of {6}*12
P/N, where N=<(s1*s0*s2)^3*s1*s2, s0*s1*s0*(s2*s1*s0*s1)^2*s2*s1> of order 8
18 facets
- 18 of {4}*8
12 vertex figures
- 12 of {6}*12
P/N, where N=<(s0*s1)^2*(s2*s1*s0*s1)^2*s2, s0*s1*s0*(s2*s1*s0*s1)^2*s2*s1, s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 8
18 facets
- 18 of {4}*8
12 vertex figures
- 12 of {6}*12
P/N, where N=<(s0*s1*s2*s1)^2, s0*(s2*s1)^2*s0*(s1*s2)^2> of order 12
12 facets
- 12 of {4}*8
8 vertex figures
- 8 of {6}*12
P/N, where N=<s0*(s1*s0*s2)^3*s1*s2, s0*(s1*s2)^2*s1*s0*(s2*s1)^2*s2> of order 16
9 facets
- 9 of {4}*8
6 vertex figures
- 6 of {6}*12
P/N, where N=<(s1*s0*s2)^3*s1*s2, s0*s1*s0*(s2*s1*s0*s1)^2*s2*s1, s0*(s1*s2)^2*s1*s0*(s1*s2)^3> of order 16
9 facets
- 9 of {4}*8
6 vertex figures
- 6 of {6}*12
Representations
Permutation Representation (GAP)
s0 := ( 9,13)(10,14)(11,15)(12,16);; s1 := ( 2, 5)( 3, 9)( 4,13)( 7,10)( 8,14)(12,15);; s2 := ( 1, 5)( 2, 8)( 3, 7)( 4, 6)(10,12)(14,16);; 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,
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*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*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,
s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(16)!( 9,13)(10,14)(11,15)(12,16); s1 := Sym(16)!( 2, 5)( 3, 9)( 4,13)( 7,10)( 8,14)(12,15); s2 := Sym(16)!( 1, 5)( 2, 8)( 3, 7)( 4, 6)(10,12)(14,16); 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, 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*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*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, s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2 >;
References
None.
to this polytope.