Overview
- Group
- SmallGroup(1920,240995)
- Rank
- 4
- Schläfli Type
- {5,5,4}
- Vertices, edges, …
- 6, 120, 96, 32
- Order of s0s1s2s3
- 6
- Order of s0s1s2s3s2s1
- 4
- Also known as
- if this polytope has a name.
Special Properties
- Non-Orientable
- Flat
Quotients maximal quotients in bold
16-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=<s1*s0*(s1*s2)^2*(s3*s2*s1)^2*s0*s1> of order 2
16 facets
- 16 of {5,5}*60
6 vertex figures
P/N, where N=<(s2*s3)^2, (s0*s1*s2*s3*s2*s1)^2> of order 4
8 facets
- 8 of {5,5}*60
6 vertex figures
- 6 of 4-fold non-regular quotient of {5,4}*320
P/N, where N=<s1*s2*s3*s2*s1*s3, s2*s1*s2*s3*s2*s1*s3*s2> of order 4
8 facets
- 8 of {5,5}*60
6 vertex figures
P/N, where N=<s0*(s1*s2)^2*(s3*s2*s1)^2*s0, (s1*s2)^2*(s1*s3*s2)^2*s1*s2> of order 4
8 facets
- 8 of {5,5}*60
6 vertex figures
P/N, where N=<(s1*s0*s1*s2*s3*s2)^2, (s0*s1)^2*s2*s3*s2*(s1*s0)^2*s2*s3*s2> of order 4
8 facets
- 8 of {5,5}*60
6 vertex figures
P/N, where N=<s1*s2*s3*s2*s1*(s2*s3)^2, (s0*s1)^2*s2*s3*s2*(s1*s0)^2*s3> of order 4
8 facets
- 8 of {5,5}*60
6 vertex figures
P/N, where N=<s0*(s1*s2)^2*(s3*s2*s1)^2*s0*s3, (s1*s2)^2*(s1*s3*s2)^2*s1*s2*s3> of order 4
8 facets
- 8 of {5,5}*60
6 vertex figures
P/N, where N=<(s2*s3)^2, (s1*s2)^2*(s3*s2*s1)^2*s3, (s0*s1*s2*s3*s2*s1)^2> of order 8
4 facets
- 4 of {5,5}*60
6 vertex figures
- 6 of 8-fold non-regular quotient of {5,4}*320
P/N, where N=<s1*s2*s3*s2*s1*s3, s2*s1*s2*s3*s2*s1*s3*s2, s0*(s1*s2)^2*(s3*s2*s1)^2*s0*s3> of order 8
4 facets
- 4 of {5,5}*60
6 vertex figures
Representations
Permutation Representation (GAP)
s0 := ( 1, 2)( 3, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(13,18)(14,19)(15,17)(16,20);; s1 := ( 1, 5)( 2, 7)( 3, 8)( 4, 6)( 9,13)(10,14)(11,16)(12,15)(17,19)(18,20);; s2 := ( 1, 4)( 2, 3)( 5,13)( 6,14)( 7,15)( 8,16)( 9,18)(10,20)(11,17)(12,19);; s3 := ( 1, 4)( 2, 3)( 5, 6)( 7, 8)( 9,12)(10,11)(13,15)(14,16)(17,18)(19,20);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s2*s0*s1*s2*s0*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s0*s3*s2*s1*s2*s1*s0*s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(20)!( 1, 2)( 3, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(13,18)(14,19)(15,17)(16,20); s1 := Sym(20)!( 1, 5)( 2, 7)( 3, 8)( 4, 6)( 9,13)(10,14)(11,16)(12,15)(17,19)(18,20); s2 := Sym(20)!( 1, 4)( 2, 3)( 5,13)( 6,14)( 7,15)( 8,16)( 9,18)(10,20)(11,17)(12,19); s3 := Sym(20)!( 1, 4)( 2, 3)( 5, 6)( 7, 8)( 9,12)(10,11)(13,15)(14,16)(17,18)(19,20); poly := sub<Sym(20)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s0*s1*s2*s0*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s0*s3*s2*s1*s2*s1*s0*s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s0*s1*s2*s1 >;
References
None.
to this polytope.