Overview
- Group
- SmallGroup(1152,157849)
- Rank
- 3
- Schläfli Type
- {12,4}
- Vertices, edges, …
- 144, 288, 48
- 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=<s1*s0*(s2*(s1*s0)^2)^2*s2*s1*s2> of order 2
24 facets
- 24 of {12}*24
72 vertex figures
- 72 of {4}*8
P/N, where N=<s1*s0*s2*(s1*s0)^2*s2*(s1*s0)^4*(s1*s2)^2> of order 2
24 facets
- 24 of {12}*24
72 vertex figures
- 72 of {4}*8
P/N, where N=<s0*s2*(s1*s0)^5*s1*s2, (s0*s1)^2*s0*s2*(s1*s0)^3*s2*s1*s0*s1> of order 4
14 facets
36 vertex figures
- 36 of {4}*8
P/N, where N=<(s1*s0)^3*s2*(s1*s0)^2*s1*s2, (s0*s1)^3*s0*s2*(s1*s0)^3*s2> of order 4
12 facets
- 12 of {12}*24
36 vertex figures
- 36 of {4}*8
P/N, where N=<(s0*s1)^6, (s0*s1)^2*s0*s2*(s1*s0)^2*s1*s2*s1> of order 4
14 facets
36 vertex figures
- 36 of {4}*8
P/N, where N=<(s0*s1)^6, s1*s2*s1*s0*s2*(s1*s0)^5*s2*s1*s2> of order 4
18 facets
36 vertex figures
- 36 of {4}*8
P/N, where N=<(s0*s1)^4, s0*s2*(s1*s0)^2*s2*(s1*s0)^4*s2*s1*s2> of order 6
10 facets
24 vertex figures
- 24 of {4}*8
P/N, where N=<(s0*s1)^6, s0*(s1*s0*s2)^3*s1*s2, (s0*s2*s1)^4> of order 8
8 facets
18 vertex figures
- 18 of {4}*8
P/N, where N=<(s0*s1)^6, (s0*s1)^2*s0*s2*(s1*s0)^2*s1*s2*s1, s0*s2*(s1*s0)^5*s1*s2> of order 8
10 facets
18 vertex figures
- 18 of {4}*8
P/N, where N=<s0*s2*(s1*s0)^2*s1*s2, (s0*s1)^2*s0*s2*(s1*s0)^3*s2*s1*s0*s1> of order 8
11 facets
18 vertex figures
- 18 of {4}*8
Representations
Permutation Representation (GAP)
s0 := ( 3, 4)( 7, 8)( 9,13)(10,14)(11,16)(12,15);; s1 := ( 1, 3)( 2, 4)( 5,15)( 6,16)( 7,13)( 8,14)( 9,11)(10,12);; s2 := ( 2, 5)( 3, 9)( 4,13)( 7,10)( 8,14)(12,15);; 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,
s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(16)!( 3, 4)( 7, 8)( 9,13)(10,14)(11,16)(12,15); s1 := Sym(16)!( 1, 3)( 2, 4)( 5,15)( 6,16)( 7,13)( 8,14)( 9,11)(10,12); s2 := Sym(16)!( 2, 5)( 3, 9)( 4,13)( 7,10)( 8,14)(12,15); 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, s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References
None.
to this polytope.