Overview
- Group
- SmallGroup(1920,240595)
- Rank
- 4
- Schläfli Type
- {4,10,10}
- Vertices, edges, …
- 4, 48, 120, 24
- Order of s0s1s2s3
- 12
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
4-fold
8-fold
16-fold
60-fold
120-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 1, 6)( 2,14)( 3, 5)( 4,15)( 7,11)( 8,12)( 9,13)(10,16);; s1 := ( 1,15)( 2, 9)( 3,13)( 4, 8)( 5,11)( 6,10)( 7,14)(12,16)(18,21)(19,20);; s2 := ( 1, 7)( 2, 4)( 3,16)( 5,10)( 6,11)( 8, 9)(12,13)(14,15)(17,21)(18,20);; s3 := ( 1,16)( 2, 9)( 3, 7)( 4, 8)( 5,11)( 6,10)(12,15)(13,14)(18,19)(20,21);; 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, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2,
s1*s2*s1*s2*s3*s2*s3*s2*s1*s2*s1*s2*s3*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(21)!( 1, 6)( 2,14)( 3, 5)( 4,15)( 7,11)( 8,12)( 9,13)(10,16); s1 := Sym(21)!( 1,15)( 2, 9)( 3,13)( 4, 8)( 5,11)( 6,10)( 7,14)(12,16)(18,21)(19,20); s2 := Sym(21)!( 1, 7)( 2, 4)( 3,16)( 5,10)( 6,11)( 8, 9)(12,13)(14,15)(17,21)(18,20); s3 := Sym(21)!( 1,16)( 2, 9)( 3, 7)( 4, 8)( 5,11)( 6,10)(12,15)(13,14)(18,19)(20,21); poly := sub<Sym(21)|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, s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2, s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, s1*s2*s1*s2*s3*s2*s3*s2*s1*s2*s1*s2*s3*s2*s3*s2 >;
References
None.
to this polytope.