Overview
- Group
- SmallGroup(120,38)
- Rank
- 3
- Schläfli Type
- {15,4}
- Vertices, edges, …
- 15, 30, 4
- Order of s0s1s2
- 15
- Order of s0s1s2s1
- 4
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Non-Orientable
- Flat
- Self-Petrie
Quotients maximal quotients in bold
5-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
5-fold
6-fold
7-fold
8-fold
- {30,4}*960a
- {15,8}*960a
- {30,8}*960a
- {120,4}*960c
- {120,4}*960d
- {60,4}*960b
- {30,4}*960b
- {60,4}*960c
- {30,8}*960b
- {30,8}*960c
9-fold
10-fold
11-fold
12-fold
13-fold
14-fold
15-fold
16-fold
- {60,4}*1920b
- {60,4}*1920c
- {15,8}*1920a
- {30,8}*1920a
- {60,8}*1920c
- {60,8}*1920d
- {30,8}*1920b
- {30,8}*1920c
- {240,4}*1920c
- {240,4}*1920d
- {60,4}*1920d
- {60,8}*1920e
- {60,8}*1920f
- {30,4}*1920a
- {30,8}*1920d
- {30,8}*1920e
- {30,8}*1920f
- {60,8}*1920g
- {60,8}*1920h
- {120,4}*1920c
- {120,4}*1920d
- {30,8}*1920g
- {60,4}*1920e
- {120,4}*1920e
- {30,4}*1920b
- {120,4}*1920f
- {15,4}*1920b
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 5, 7)( 6, 8)( 9,10)(11,15)(12,14)(13,16)(17,19)(18,20);; s1 := ( 1, 2)( 3, 5)( 4,13)( 6, 9)( 8,18)(10,14)(11,12)(15,17)(16,19);; s2 := ( 1, 4)( 2, 6)( 3, 8)( 5,11)( 7,15)( 9,10)(12,16)(13,14)(17,20)(18,19);; 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,
s2*s1*s0*s2*s1*s2*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(20)!( 2, 3)( 5, 7)( 6, 8)( 9,10)(11,15)(12,14)(13,16)(17,19)(18,20); s1 := Sym(20)!( 1, 2)( 3, 5)( 4,13)( 6, 9)( 8,18)(10,14)(11,12)(15,17)(16,19); s2 := Sym(20)!( 1, 4)( 2, 6)( 3, 8)( 5,11)( 7,15)( 9,10)(12,16)(13,14)(17,20)(18,19); poly := sub<Sym(20)|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, s2*s1*s0*s2*s1*s2*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.