Overview
- Group
- SmallGroup(1920,240560)
- Rank
- 3
- Schläfli Type
- {8,6}
- Vertices, edges, …
- 160, 480, 120
- Order of s0s1s2
- 40
- 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=<s0*s1*s0*(s2*s1)^2*s0*s2*s1*s0*(s1*s2)^3> of order 2
60 facets
- 60 of {8}*16
80 vertex figures
- 80 of {6}*12
P/N, where N=<s0*s1*s0*(s2*s1)^2*s0*s2*s1*s0*(s2*s1)^2*s2> of order 2
60 facets
- 60 of {8}*16
80 vertex figures
- 80 of {6}*12
P/N, where N=<s0*s2*s1*s0*(s1*s2)^2*(s1*s0*s2)^2*s1*s2> of order 2
60 facets
- 60 of {8}*16
80 vertex figures
- 80 of {6}*12
P/N, where N=<s1*s0*s2*s1*s0*s1*(s2*s1*s0)^2*s2*s1> of order 3
40 facets
- 40 of {8}*16
64 vertex figures
P/N, where N=<s0*s1*s0*(s2*s1)^2*s0*s2*s1*s0*(s2*s1)^2*s2, s0*(s2*s1)^2*s0*s1*s0*(s2*s1)^2*s0*s2*s1*s2> of order 4
30 facets
- 30 of {8}*16
40 vertex figures
- 40 of {6}*12
P/N, where N=<(s0*(s2*s1)^2*s0*s1)^2*s2> of order 4
30 facets
- 30 of {8}*16
40 vertex figures
- 40 of {6}*12
P/N, where N=<(s0*s2*s1)^2*s0*(s1*s2)^2*s1*s0*s1*s2> of order 4
30 facets
- 30 of {8}*16
40 vertex figures
- 40 of {6}*12
P/N, where N=<s0*s1*s0*(s2*s1)^2*s0*s2*s1*s0*(s2*s1)^2*s2, (s0*s2*s1)^2*s0*(s1*s2)^2*s1*s0*s2*s1*s2> of order 4
30 facets
- 30 of {8}*16
40 vertex figures
- 40 of {6}*12
P/N, where N=<s0*s1*s0*(s2*s1)^2*(s0*s1)^2*s2*s1*s2> of order 5
24 facets
- 24 of {8}*16
32 vertex figures
- 32 of {6}*12
P/N, where N=<s1*s0*(s2*s1)^2*s0*s2*s1*s2, s0*s1*s0*(s2*s1)^2*s0*s2*s1*s0*s2> of order 6
20 facets
- 20 of {8}*16
32 vertex figures
P/N, where N=<(s0*s1)^3*(s2*s1)^2*s0*s2*s1*s2, (s0*s1)^2*(s2*s1)^2*s0*s2*s1*s0*s1*s2> of order 6
20 facets
- 20 of {8}*16
32 vertex figures
P/N, where N=<(s0*(s2*s1)^2)^2, s1*s0*(s2*s1)^2*s0*s2*s1*s2> of order 10
12 facets
- 12 of {8}*16
16 vertex figures
- 16 of {6}*12
P/N, where N=<(s0*s1)^3*(s2*s1)^2*s0*s2*s1*s2, s0*s1*(s2*s1*s0)^2*(s2*s1)^2*s0*s1> of order 10
12 facets
- 12 of {8}*16
16 vertex figures
- 16 of {6}*12
P/N, where N=<(s0*s1*s2*s1)^3, s0*(s1*s2)^2*s1*s0*s1*s2*s1*s0*s1> of order 10
12 facets
- 12 of {8}*16
16 vertex figures
- 16 of {6}*12
P/N, where N=<s0*(s2*s1)^2*s0*(s1*s2)^2, s2*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 12
10 facets
- 10 of {8}*16
24 vertex figures
Representations
Permutation Representation (GAP)
s0 := ( 3, 5)( 6,14)( 7,15)( 8,17)( 9,16)(10,18)(11,19)(12,21)(13,20)(22,30)(23,31)(24,33)(25,32)(26,34)(27,35)(28,37)(29,36);; s1 := ( 2, 3)( 4, 5)( 6,26)( 7,27)( 8,29)( 9,28)(10,22)(11,23)(12,25)(13,24)(14,36)(15,37)(16,34)(17,35)(18,32)(19,33)(20,30)(21,31);; s2 := ( 1, 2)( 6,10)( 7,11)( 8,12)( 9,13)(14,18)(15,19)(16,20)(17,21)(22,26)(23,27)(24,28)(25,29)(30,34)(31,35)(32,36)(33,37);; 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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(37)!( 3, 5)( 6,14)( 7,15)( 8,17)( 9,16)(10,18)(11,19)(12,21)(13,20)(22,30)(23,31)(24,33)(25,32)(26,34)(27,35)(28,37)(29,36); s1 := Sym(37)!( 2, 3)( 4, 5)( 6,26)( 7,27)( 8,29)( 9,28)(10,22)(11,23)(12,25)(13,24)(14,36)(15,37)(16,34)(17,35)(18,32)(19,33)(20,30)(21,31); s2 := Sym(37)!( 1, 2)( 6,10)( 7,11)( 8,12)( 9,13)(14,18)(15,19)(16,20)(17,21)(22,26)(23,27)(24,28)(25,29)(30,34)(31,35)(32,36)(33,37); poly := sub<Sym(37)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 >;
References
None.
to this polytope.