Overview
- Group
- SmallGroup(1440,5924)
- Rank
- 6
- Schläfli Type
- {2,10,2,6,3}
- Vertices, edges, …
- 2, 10, 10, 6, 9, 3
- Order of s0s1s2s3s4s5
- 30
- Order of s0s1s2s3s4s5s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
5-fold
6-fold
15-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 5, 6)( 7, 8)( 9,10)(11,12);; s2 := ( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,12);; s3 := (16,17)(18,19)(20,21);; s4 := (13,16)(14,20)(15,18)(19,21);; s5 := (13,14)(16,19)(17,18)(20,21);; poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s4*s5*s4*s5*s4*s5, s3*s4*s5*s3*s4*s3*s4*s5*s3*s4,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(21)!(1,2); s1 := Sym(21)!( 5, 6)( 7, 8)( 9,10)(11,12); s2 := Sym(21)!( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,12); s3 := Sym(21)!(16,17)(18,19)(20,21); s4 := Sym(21)!(13,16)(14,20)(15,18)(19,21); s5 := Sym(21)!(13,14)(16,19)(17,18)(20,21); poly := sub<Sym(21)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5*s4*s5, s3*s4*s5*s3*s4*s3*s4*s5*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;