Overview
- Group
- SmallGroup(1920,240505)
- Rank
- 3
- Schläfli Type
- {20,4}
- Vertices, edges, …
- 240, 480, 48
- Order of s0s1s2
- 12
- Order of s0s1s2s1
- 6
- 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
8-fold
16-fold
60-fold
120-fold
240-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*s1*s2)^2*s1*s0*s2*s1*s2> of order 2
24 facets
- 24 of {20}*40
120 vertex figures
- 120 of {4}*8
P/N, where N=<(s0*s1)^3*s2*(s1*s0)^3*s2*s1*s0*s2*s1*s2> of order 2
24 facets
- 24 of {20}*40
120 vertex figures
- 120 of {4}*8
P/N, where N=<(s0*s1)^3*s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 2
24 facets
- 24 of {20}*40
120 vertex figures
- 120 of {4}*8
P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*s2*s1> of order 2
24 facets
- 24 of {20}*40
120 vertex figures
- 120 of {4}*8
P/N, where N=<(s0*s1)^3*s2*(s1*s0)^2*s1*s2*s1*s0*s2*s1*s2> of order 2
24 facets
- 24 of {20}*40
120 vertex figures
- 120 of {4}*8
P/N, where N=<s2*(s1*s0)^2*s1*(s2*s1*s0)^2*s1*s2> of order 2
24 facets
- 24 of {20}*40
128 vertex figures
P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*s2*s1, s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1*s2> of order 4
12 facets
- 12 of {20}*40
60 vertex figures
- 60 of {4}*8
P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*s2*s1, (s0*s1)^2*(s2*s1*s0)^2*s1*s2*(s1*s0)^2*s1*s2> of order 4
12 facets
- 12 of {20}*40
60 vertex figures
- 60 of {4}*8
P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*s2*s1, (s1*s0)^2*s1*(s2*s1*s0)^2*s1> of order 4
12 facets
- 12 of {20}*40
68 vertex figures
P/N, where N=<(s1*s0*s1*s2)^2, (s0*s1)^3*s2*(s1*s0)^3*s1*s2*s1> of order 6
8 facets
- 8 of {20}*40
40 vertex figures
- 40 of {4}*8
P/N, where N=<(s1*s0*s1*s2)^2, s0*(s1*s0*s2)^3*(s1*s0)^2*s1*s2> of order 6
8 facets
- 8 of {20}*40
40 vertex figures
- 40 of {4}*8
P/N, where N=<(s1*s0*s1*s2)^2, (s0*s1)^3*s2*(s1*s0)^4*s2*s1> of order 6
8 facets
- 8 of {20}*40
40 vertex figures
- 40 of {4}*8
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, s0*s1*s0*s2*(s1*s0)^2*s2*s1> of order 10
8 facets
24 vertex figures
- 24 of {4}*8
P/N, where N=<s0*s2*(s1*s0)^3*s1*s2, (s0*s1)^3*(s0*s2*s1)^3*s2> of order 10
8 facets
24 vertex figures
- 24 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, (s0*s1)^2*(s2*s1*s0)^2> of order 10
8 facets
32 vertex figures
P/N, where N=<s0*s2*(s1*s0)^3*s1*s2, (s1*s0)^3*(s2*s1*s0)^2*s2*s1*s2> of order 10
8 facets
24 vertex figures
- 24 of {4}*8
Representations
Permutation Representation (GAP)
s0 := ( 1, 8)( 2, 4)( 3, 5)( 6, 7)(10,13)(11,12);; s1 := ( 1, 4)( 2, 7)( 3, 8)( 5, 6)( 9,11)(10,12);; s2 := ( 2, 4)( 3, 5)(11,12);; 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*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*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*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(13)!( 1, 8)( 2, 4)( 3, 5)( 6, 7)(10,13)(11,12); s1 := Sym(13)!( 1, 4)( 2, 7)( 3, 8)( 5, 6)( 9,11)(10,12); s2 := Sym(13)!( 2, 4)( 3, 5)(11,12); poly := sub<Sym(13)|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*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*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*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1, s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1 >;
References
None.
to this polytope.