Overview
- Group
- SmallGroup(1440,5853)
- Rank
- 3
- Schläfli Type
- {10,6}
- Vertices, edges, …
- 120, 360, 72
- Order of s0s1s2
- 30
- Order of s0s1s2s1
- 10
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
12-fold
24-fold
60-fold
120-fold
180-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*s2*(s1*s0)^3*s2*(s1*s0)^2*s2*s1*s2> of order 2
36 facets
- 36 of {10}*20
60 vertex figures
- 60 of {6}*12
P/N, where N=<(s0*s1)^2*s0*s2*(s1*s0)^2*s2*s1*s0*s1*s2> of order 2
36 facets
- 36 of {10}*20
60 vertex figures
- 60 of {6}*12
P/N, where N=<((s1*s0)^3*s2)^2*(s1*s0)^2*s1*s2> of order 2
36 facets
- 36 of {10}*20
60 vertex figures
- 60 of {6}*12
P/N, where N=<(s1*s0)^3*s1*s2*s1*s0*(s2*(s1*s0)^2)^2*s1*s2> of order 2
36 facets
- 36 of {10}*20
60 vertex figures
- 60 of {6}*12
P/N, where N=<(s0*s1)^4*s2*(s1*s0)^2*s2> of order 3
24 facets
- 24 of {10}*20
40 vertex figures
- 40 of {6}*12
P/N, where N=<(s0*s1)^2*s0*s2*(s1*s0)^2*s2*s1*s0*s1, s0*s1*s0*s2*(s1*s0)^4*s2*s1> of order 4
18 facets
- 18 of {10}*20
30 vertex figures
- 30 of {6}*12
P/N, where N=<(s0*s1)^3*(s2*s1*s0)^3*s1, (s0*s1)^2*s2*s1*s0*s2*(s1*s0)^3*s2*s1> of order 4
18 facets
- 18 of {10}*20
30 vertex figures
- 30 of {6}*12
P/N, where N=<(s0*s1)^4*s2*(s1*s0)^2*s2, (s0*s1)^3*s2*s1*s0*s2*(s1*s0)^2*s1*s2> of order 6
12 facets
- 12 of {10}*20
20 vertex figures
- 20 of {6}*12
P/N, where N=<(s0*s1)^4*s2*(s1*s0)^2*s2, (s0*s1)^2*s0*s2*(s1*s0)^3*s1*s2> of order 6
12 facets
- 12 of {10}*20
20 vertex figures
- 20 of {6}*12
P/N, where N=<(s0*s1)^2, s0*s1*s2*(s1*s0)^3*s2*(s1*s0)^2*s1*s2> of order 10
12 facets
12 vertex figures
- 12 of {6}*12
P/N, where N=<(s0*s1)^2, s0*s2*(s1*s0)^3*s2*(s1*s0)^2*s2*s1*s2> of order 10
12 facets
12 vertex figures
- 12 of {6}*12
Representations
Permutation Representation (GAP)
s0 := ( 3, 6)( 4, 5)( 7,10)( 8, 9)(11,14)(12,15)(13,16);; s1 := ( 1, 3)( 2, 4)( 5, 8)( 6, 7)(12,16)(13,15);; s2 := ( 1, 2)( 3, 9)( 4,10)( 5, 7)( 6, 8)(11,12)(13,16)(14,15);; 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, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(16)!( 3, 6)( 4, 5)( 7,10)( 8, 9)(11,14)(12,15)(13,16); s1 := Sym(16)!( 1, 3)( 2, 4)( 5, 8)( 6, 7)(12,16)(13,15); s2 := Sym(16)!( 1, 2)( 3, 9)( 4,10)( 5, 7)( 6, 8)(11,12)(13,16)(14,15); 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, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1 >;
References
None.
to this polytope.