Overview
- Group
- SmallGroup(720,831)
- Rank
- 5
- Schläfli Type
- {3,2,30,2}
- Vertices, edges, …
- 3, 3, 30, 30, 2
- Order of s0s1s2s3s4
- 30
- Order of s0s1s2s3s4s3s2s1
- 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
10-fold
15-fold
Covers minimal covers in bold
2-fold
Representations
Permutation Representation (GAP)
s0 := (2,3);; s1 := (1,2);; s2 := ( 6, 7)( 8, 9)(10,11)(12,13)(14,17)(15,16)(18,19)(20,23)(21,22)(24,25)(26,29)(27,28)(30,33)(31,32);; s3 := ( 4,20)( 5,14)( 6,12)( 7,22)( 8,10)( 9,30)(11,16)(13,26)(15,24)(17,32)(18,21)(19,31)(23,28)(25,27)(29,33);; s4 := (34,35);; poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(35)!(2,3); s1 := Sym(35)!(1,2); s2 := Sym(35)!( 6, 7)( 8, 9)(10,11)(12,13)(14,17)(15,16)(18,19)(20,23)(21,22)(24,25)(26,29)(27,28)(30,33)(31,32); s3 := Sym(35)!( 4,20)( 5,14)( 6,12)( 7,22)( 8,10)( 9,30)(11,16)(13,26)(15,24)(17,32)(18,21)(19,31)(23,28)(25,27)(29,33); s4 := Sym(35)!(34,35); poly := sub<Sym(35)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;