Overview
- Group
- SmallGroup(160,131)
- Rank
- 3
- Schläfli Type
- {10,8}
- Vertices, edges, …
- 10, 40, 8
- Order of s0s1s2
- 40
- Order of s0s1s2s1
- 2
- Also known as
- {10,8|2}. if this polytope has another name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
4-fold
5-fold
8-fold
10-fold
20-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
5-fold
6-fold
7-fold
8-fold
- {40,8}*1280a
- {20,8}*1280a
- {40,8}*1280c
- {20,16}*1280a
- {20,16}*1280b
- {80,8}*1280a
- {80,8}*1280b
- {40,16}*1280c
- {80,8}*1280d
- {40,16}*1280d
- {40,16}*1280e
- {80,8}*1280f
- {40,16}*1280f
- {20,32}*1280a
- {20,32}*1280b
- {10,64}*1280
9-fold
10-fold
11-fold
12-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 5)( 3, 4)( 7,10)( 8, 9)(12,15)(13,14)(17,20)(18,19)(22,25)(23,24)(27,30)(28,29)(32,35)(33,34)(37,40)(38,39);; s1 := ( 1, 2)( 3, 5)( 6, 7)( 8,10)(11,17)(12,16)(13,20)(14,19)(15,18)(21,37)(22,36)(23,40)(24,39)(25,38)(26,32)(27,31)(28,35)(29,34)(30,33);; s2 := ( 1,21)( 2,22)( 3,23)( 4,24)( 5,25)( 6,26)( 7,27)( 8,28)( 9,29)(10,30)(11,36)(12,37)(13,38)(14,39)(15,40)(16,31)(17,32)(18,33)(19,34)(20,35);; 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*s0*s1*s2*s1,
s1*s2*s1*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(40)!( 2, 5)( 3, 4)( 7,10)( 8, 9)(12,15)(13,14)(17,20)(18,19)(22,25)(23,24)(27,30)(28,29)(32,35)(33,34)(37,40)(38,39); s1 := Sym(40)!( 1, 2)( 3, 5)( 6, 7)( 8,10)(11,17)(12,16)(13,20)(14,19)(15,18)(21,37)(22,36)(23,40)(24,39)(25,38)(26,32)(27,31)(28,35)(29,34)(30,33); s2 := Sym(40)!( 1,21)( 2,22)( 3,23)( 4,24)( 5,25)( 6,26)( 7,27)( 8,28)( 9,29)(10,30)(11,36)(12,37)(13,38)(14,39)(15,40)(16,31)(17,32)(18,33)(19,34)(20,35); poly := sub<Sym(40)|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*s0*s1*s2*s1, s1*s2*s1*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 >;
References
None.
to this polytope.