Overview
- Group
- SmallGroup(1152,157849)
- Rank
- 3
- Schläfli Type
- {8,6}
- Vertices, edges, …
- 96, 288, 72
- 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
- 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=<s0*(s2*s1)^2*(s0*s1)^2*s2*s1*s0*s2*s1> of order 2
36 facets
- 36 of {8}*16
48 vertex figures
- 48 of {6}*12
P/N, where N=<s2*s1*s0*(s1*s2)^2*s1*s0*s2*s1*s2, s0*s1*s0*(s2*s1)^2*(s0*s1)^2*s2*s1*s2> of order 4
18 facets
- 18 of {8}*16
28 vertex figures
P/N, where N=<(s1*s2*s1*s0)^2*s1*s2> of order 4
18 facets
- 18 of {8}*16
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
22 facets
24 vertex figures
- 24 of {6}*12
P/N, where N=<s0*s1*s2*(s1*s0)^2*s1*s2*s1*s0*s2*s1*s2, s0*(s2*s1)^2*(s0*s1)^2*s2*s1*s0*s2*s1> of order 4
18 facets
- 18 of {8}*16
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s0*s1)^4, s0*s1*s0*(s2*s1)^2*(s0*s1)^2*s2*s1*s2> of order 4
20 facets
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s1*s2)^2, (s0*s1)^3*(s2*s1)^2*s0*s2*(s1*s0)^2> of order 6
12 facets
- 12 of {8}*16
24 vertex figures
P/N, where N=<(s0*s1)^4, s0*s2*(s1*s0)^3*s1*s2, s1*s0*s2*(s1*s0)^3*s1*s2*s1> of order 8
14 facets
12 vertex figures
- 12 of {6}*12
P/N, where N=<(s0*s1)^4, (s0*s2*s1)^4, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s2*s1*s2> of order 8
12 facets
12 vertex figures
- 12 of {6}*12
P/N, where N=<s0*s1*s2*s1*s0*s1*s2*(s1*s0)^2*s2, s2*s1*s0*(s1*s2)^2*s1*s0*s2*s1*s2> of order 8
9 facets
- 9 of {8}*16
14 vertex figures
Representations
Permutation Representation (GAP)
s0 := ( 2, 5)( 3, 9)( 4,13)( 7,10)( 8,14)(12,15);; s1 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,15)(10,16)(11,13)(12,14);; s2 := ( 2, 4)( 5,13)( 6,16)( 7,15)( 8,14)(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*s1*s2*s1*s2,
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(16)!( 2, 5)( 3, 9)( 4,13)( 7,10)( 8,14)(12,15); s1 := Sym(16)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,15)(10,16)(11,13)(12,14); s2 := Sym(16)!( 2, 4)( 5,13)( 6,16)( 7,15)( 8,14)(10,12); 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1 >;
References
None.
to this polytope.