Overview
- Group
- SmallGroup(1440,5848)
- Rank
- 3
- Schläfli Type
- {20,3}
- Vertices, edges, …
- 240, 360, 36
- Order of s0s1s2
- 15
- Order of s0s1s2s1
- 20
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Non-Orientable
Quotients maximal quotients in bold
4-fold
12-fold
24-fold
60-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)^2*(s2*(s1*s0)^3*s1)^2*s2*s1*s0*s1> of order 2
18 facets
- 18 of {20}*40
120 vertex figures
- 120 of {3}*6
P/N, where N=<s0*s1*s0*s2*(s1*s0)^9*s1*s2*s1> of order 2
18 facets
- 18 of {20}*40
120 vertex figures
- 120 of {3}*6
P/N, where N=<(s0*s1)^3*(s2*(s1*s0)^2)^2*s2> of order 3
12 facets
- 12 of {20}*40
80 vertex figures
- 80 of {3}*6
P/N, where N=<s0*s2*(s1*s0)^2*s1*s2*(s1*s0)^3*s2*s1> of order 3
12 facets
- 12 of {20}*40
80 vertex figures
- 80 of {3}*6
P/N, where N=<(s0*s1)^2*(s2*(s1*s0)^3*s1)^2*s2*s1*s0*s1, ((s1*s0)^3*s1*s2)^3> of order 4
12 facets
60 vertex figures
- 60 of {3}*6
P/N, where N=<(s0*s1)^4*(s2*(s1*s0)^3*s1)^2, (s0*s1)^2*s2*(s1*s0)^7*s1*s2*s1*s0*s1> of order 4
9 facets
- 9 of {20}*40
60 vertex figures
- 60 of {3}*6
P/N, where N=<(s0*s1)^3*(s2*(s1*s0)^2)^2*s2, (s0*s1)^2*(s2*(s1*s0)^3*s1)^2*s2*s1*s0*s1> of order 6
6 facets
- 6 of {20}*40
40 vertex figures
- 40 of {3}*6
P/N, where N=<s0*s2*(s1*s0)^2*s1*s2*(s1*s0)^3*s2*s1, (s0*s1)^7*s2*(s1*s0)^3*s1*s2*s1> of order 6
6 facets
- 6 of {20}*40
40 vertex figures
- 40 of {3}*6
P/N, where N=<(s0*s1)^4, s0*s1*s0*s2*(s1*s0)^6*s1*s2*(s1*s0)^2*s1*s2> of order 10
6 facets
24 vertex figures
- 24 of {3}*6
P/N, where N=<(s1*s0)^2*s2*s1*s0*s1*s2, (s0*s1)^2*s2*(s1*s0)^2*s2> of order 10
8 facets
24 vertex figures
- 24 of {3}*6
Representations
Permutation Representation (GAP)
s0 := (2,3)(4,5)(6,7)(8,9);; s1 := (1,2)(3,4)(7,8);; s2 := (2,5)(3,4)(8,9);; 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,
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(9)!(2,3)(4,5)(6,7)(8,9); s1 := Sym(9)!(1,2)(3,4)(7,8); s2 := Sym(9)!(2,5)(3,4)(8,9); poly := sub<Sym(9)|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, s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References
None.
to this polytope.